Method and system for evaluating cardiac ischemia with an abrupt stop exercise protocol

ABSTRACT

A method of assessing cardiac ischemia in a subject to provide a measure of cardiac or cardiovascular health in that subject is described herein. The method comprises the steps of: (a) collecting a first RR-interval data set from the subject during a stage of gradually increasing heart rate (e.g., a stage of gradually increasing exercise load); (b) collecting a second RR-interval data set from the subject during a stage of gradually decreasing heart rate (e.g., a stage of gradually decreasing exercise load, or a stage of rest following an abrupt stop of exercise in a patient with coronary artery disease); (c) comparing the first RR-interval data set to the second RR-interval data set to determine the difference between the data sets; and (d) generating from the comparison of step (c) a measure of cardiac ischemia during exercise in the subject. A greater difference between the first and second data sets indicates greater cardiac ischemia and lesser cardiac or cardiovascular health in the subject. The data sets are collected in such a manner that they reflect almost exclusively the conduction in the heart muscle and minimize the effect on the data sets of rapid transients due to autonomic nervous system and hormonal control.

RELATED APPLICATIONS

This application is a continuation-in-part of application Ser. No.09/891,910, filed Jun. 26, 2001, which in turn is is acontinuation-in-part of copending application Ser. No. 09/603,286, filedJun. 26, 2000 now U.S. Pat. No. 6,361,503, the disclosures of both ofwhich are incorporated by reference herein in its entirety.

FIELD OF THE INVENTION

The present invention relates to non-invasive high-resolutiondiagnostics of cardiac ischemia based on processing of body-surfaceelectrocardiogram (ECG) data. The invention's quantitative method ofassessment of cardiac ischemia may simultaneously indicate both cardiachealth itself and cardiovascular system health in general.

BACKGROUND OF THE INVENTION

Heart attacks and other ischemic events of the heart are among theleading causes of death and disability in the United States. In general,the susceptibility of a particular patient to heart attack or the likecan be assessed by examining the heart for evidence of ischemia(insufficient blood flow to the heart tissue itself resulting in aninsufficient oxygen supply) during periods of elevated heart activity.Of course, it is highly desirable that the measuring technique besufficiently benign to be carried out without undue stress to the heart(the condition of which might not yet be known) and without unduediscomfort to the patient.

The cardiovascular system responds to changes in physiological stress byadjusting the heart rate, which adjustments can be evaluated bymeasuring the surface ECG R-R intervals. The time intervals betweenconsecutive R waves indicate the intervals between the consecutiveheartbeats (RR intervals). This adjustment normally occurs along withcorresponding changes in the duration of the ECG QT intervals, whichcharacterize the duration of electrical excitation of cardiac muscle andrepresent the action potential duration averaged over a certain volumeof cardiac muscle (FIG. 1). Generally speaking, an average actionpotential duration measured as the QT interval at each ECG lead may beconsidered as an indicator of cardiac systolic activity varying in time.

Recent advances in computer technology have led to improvements inautomatic analyzing of heart rate and QT interval variability. It iswell known now that the QT interval's variability (dispersion)observations performed separately or in combination with heart rate (orRR-interval) variability analysis provides an effective tool for theassessment of individual susceptibility to cardiac arrhythmias (B.Surawicz, J. Cardiovasc. Electrophysiol, 1996, 7, 777-784). Applicationsof different types of QT and some other interval variability tosusceptibility to cardiac arrhythmias are described in U.S. Patents byChamoun U.S. Pat. No. 5,020,540, 1991; Wang U.S. Pat. No. 4,870,974,1989; Kroll et al. U.S. Pat. No. 5,117,834, 1992; Henkin et al. U.S.Pat. No. 5,323,783, 1994; Xue et al. U.S. Pat. No. 5,792,065, 1998;Lander U.S. Pat. No. 5,827,195, 1998; Lander et al. U.S. Pat. No.5,891,047, 1999; Hojum et al. U.S. Pat. No. 5,951,484, 1999).

It was recently found that cardiac electrical instability can be alsopredicted by linking the QT—dispersion observations with the ECG T-wavealternation analysis (Verrier et al., U.S. Pat. Nos. 5,560,370;5,842,997; 5,921,940). This approach is somewhat useful in identifyingand managing individuals at risk for sudden cardiac death. The authorsreport that QT interval dispersion is linked with risk for arrhythmiasin patients with long QT syndrome. However, QT interval dispersionalone, without simultaneous measurement of T—wave alternation, is saidto be a less accurate predictor of cardiac electrical instability (U.S.Pat. No. 5,560,370 at column 6, lines 4-15).

Another application of the QT interval dispersion analysis forprediction of sudden cardiac death is developed by J. Sarma (U.S. Pat.No. 5,419,338). He describes a method of an autonomic nervous systemtesting that is designed to evaluate the imbalances between bothparasympathetic and sympathetic controls on the heart and, thus, toindicate a predisposition for sudden cardiac death.

The same author suggested that an autonomic nervous system testingprocedure might be designed on the basis of the QT hysteresis (J. Sarmaet al., PACE 10, 485-491 (1988)). Hysteresis between exercise andrecovery was observed, and was attributed to sympatho-adrenal activityin the early post-exercise period. Such an activity was revealed in thecourse of QT interval adaptation to changes in the RR interval duringexercise with rapid variation of the load.

The influence of sympatho-adrenal activity and the sharp dependence ofthis hysteresis on the time course of abrupt QT interval adaptation torapid changes in the RR interval dynamics radically overshadows themethod's susceptibility to the real ischemic-like changes of cardiacmuscle electrical parameters and cardiac electrical conduction.Therefore, this type of hysteresis phenomenon would not be useful inassessing the health of the cardiac muscle itself, or in assessingcardiac ischemia.

A similar sympatho-adrenal imbalance type hysteresis phenomenon wasobserved by A. Krahn et al. (Circulation 96, 1551-1556 (1997)(see FIG. 2therein)). The authors state that this type of QT interval hysteresismay be a marker for long-QT syndrome. However, long-QT syndromehysteresis is a reflection of a genetic defect of intracardiac ionchannels associated with exercise or stress-induced syncope or suddendeath. Therefore, similar to the example described above, although dueto two different reasons, it also does not involve a measure of cardiacischemia or cardiac muscle ischemic health.

A conventional non-invasive method of assessing coronary artery diseasesassociated with cardiac ischemia is based on the observation ofmorphological changes in a surface electrocardiogram duringphysiological exercise (stress test). A change of the ECG morphology,such as an inversion of the T-wave, is known to be a qualitativeindication of ischemia. The dynamics of the ECG ST-segments arecontinuously monitored while the shape and slope, as well as ST-segmentelevation or depression, measured relative to an average base line, arealtering in response to exercise load. A comparison of any of thesechanges with average values of monitored ST segment data provides anindication of insufficient coronary blood circulation and developingischemia. Despite a broad clinical acceptance and the availability ofcomputerized Holter monitor-like devices for automatic ST segment dataprocessing, the diagnostic value of this method is limited due to itslow sensitivity and low resolution. Since the approach is specificallyreliable primarily for ischemic events associated with relatively highcoronary artery occlusion, its widespread use often results in falsepositives, which in turn may lead to unnecessary and more expensive,invasive cardiac catheterization.

Relatively low sensitivity and low resolution, which are fundamentaldisadvantages of the conventional ST-segment depression method, areinherent in such method's being based on measuring an amplitude of abody surface ECG signal, which signal by itself does not accuratelyreflect changes in an individual cardiac cell's electrical parametersnormally changing during an ischemic cardiac event. A body surface ECGsignal is a composite determined by action potentials aroused fromdischarge of hundred of thousands of individual excitable cardiac cells.When electrical activity of excitable cells slightly and locally altersduring the development of exercise-induced local ischemia, itselectrical image in the ECG signal on the body surface is significantlyovershadowed by the aggregate signal from the rest of the heart.Therefore, regardless of physiological conditions, such as stress orexercise, conventional body surface ECG data processing is characterizedby a relatively high threshold (lower sensitivity) of detectableischemic morphological changes in the ECG signal. An accurate andfaultless discrimination of such changes is still a challenging signalprocessing problem.

Accordingly, an object of the present invention is to provide anon-invasive technique for detecting and measuring cardiac ischemia in apatient.

Another object of the invention is to provide a technique for detectingand measuring cardiac ischemia, which technique is not undulyuncomfortable or stressful for the patient.

Another object of the invention is to provide a technique for detectingand measuring cardiac ischemia, which technique may be implemented withrelatively simple equipment.

Still another object of the invention is to provide a technique fordetecting and measuring cardiac ischemia, which technique is sensitiveto low levels of such ischemia.

SUMMARY OF THE INVENTION

The present invention overcomes the deficiencies in the conventionalST-segment analysis. Although still based on the processing of a bodysurface ECG signal, it nevertheless provides a highly sensitive and highresolution method for distinguishing changes in cardiac electricalconduction associated with developing cardiac ischemia. In addition tothe significant cardiac ischemic changes detectable by the conventionalmethod, the present invention allows one to determine much smallerischemia-induced conditions and alterations in cardiac electricalconduction. Thus, unlike a conventional ST-segment depression ischemicanalysis, the method of the present invention opens up opportunities todetect low-level cardiac ischemia (undetectable via the regularST-segment method) and also to resolve and monitor small variations ofcardiac ischemia. In particular, individuals who would be considered ofthe same level of cardiac and cardiovascular health according to aconventional ECG evaluation (an ST-depression method), will havedifferent measurements if compared according to the method of thepresent invention, and the cardiac and cardiovascular health of anindividual can be quantitatively evaluated, compared and monitored byrepeated applications of the method of the present invention.

The present invention is based in part on the discovery that, undercertain physiological conditions, QT- and/or RR-interval data sets maybe interpreted as representing composite dispersion-restitution curves,which characterize the basic dynamic properties of the medium (in thiscase, cardiac muscle). Indeed, if rapid interval adaptation facilitatedby sympatho-adrenal activity occurs much faster than gradual heart ratechanges following slow alteration of external physiological conditions,then the interval may be considered primarily as a function of a heartrate and/or a preceding cardiac cycle length and does not substantiallydepend on time-dependent sympatho-adrenal transients. In such a case aparticular interval data set determines a time-independent,dispersion-like, quasi-stationary curve which does not substantiallydepend on rapid adaptational transients and depends primarily on mediumelectrical parameters.

Based on this discovery, the present invention provides a highlysensitive and high resolution method of assessing cardiac ischemia. Thismethod allows one to detect comparatively small alterations of cardiacmuscle electrical excitation properties that develop during even amoderate ischemic condition. For example, consider a gradual heart rateadjustment in a particular human subject in response to slow(quasi-stationary), there-and-back changes of external physiologicalconditions. Ideally, when a cardiac muscle is supplied by a sufficientamount of oxygen during both gradually increasing and graduallydecreasing heart rate stages, the corresponding, there-and-back,quasi-stationary interval curves which result should be virtuallyidentical. However, if ischemia exists, even if only to a very minorextent, there will be alterations of cardiac muscle repolarization andexcitation properties for the human subject with the result that oneobserves a specific quasi-stationary hysteresis loop. Unlikenon-stationary loops (J. Sarma et al., supra (1987); A. Krahn et al.,supra (1997)), the quasi-stationary hystereses of the present inventiondo not vary substantially versus the course of sympatho-adrenal intervaladjustment. The domains and shapes of these loops are not significantlyaffected by time-dependent transients rapidly decaying during atransition from one particular heart rate to another; instead, theydepend primarily on ischemia-induced changes of medium parameters. Thedomain encompassed by such a quasi-stationary hysteresis loop and itsshape represent a new quantitative characteristics that indicate cardiacmuscle health itself and the health of the cardiovascular system ingeneral. Moreover, any measure of the shape and/or domain enclosed inthe hysteresis loop (a measure of a set as defined in the integraltheory) possesses the property that any expansion of the domain resultsin an increase of the measure. Any such mathematical measure can betaken as the new characteristics of cardiac health mentioned above. Anarbitrary monotonic function of such a measure would still represent thesame measure in another, transformed scale.

A first aspect of the present invention is a method of assessing cardiacischemia in a subject to provide a measure of cardiovascular health inthat subject. The method comprises the steps of:

(a) collecting a first RR-interval data set (e.g., a first QT- andRR-interval data set) from the subject during a stage of graduallyincreasing heart rate;

(b) collecting a second RR-interval data set (e.g., a second QT- andRR-interval data set) from the subject during a stage of graduallydecreasing heart rate;

(c) comparing said first interval data set to the second interval dataset to determine the difference between the data sets; and

(d) generating from the comparison of step (c) a measure of cardiacischemia during exercise in said subject, wherein a greater differencebetween said first and second data sets indicates greater cardiacischemia and lesser cardiovascular health in said subject.

During the periods of gradually increasing and gradually decreasingheart rate the effect of the sympathetic, parasympathetic, and hormonalcontrol on formation of the hysteresis loop is sufficiently small,minimized or controlled so that the ischemic changes are readilydetectable. This maintenance is achieved by effecting a gradual increaseand gradual decrease in the heart rate, such as, for example, bycontrolling the heart rate through pharmacological intervention, bydirect electrical stimulation of the heart, or by gradually increasingand gradually decreasing exercise loads.

Accordingly, the foregoing method can be implemented in a variety ofdifferent ways. A particular embodiment comprises the steps of:

(a) collecting a first RR-interval data set (e.g., a first QT- andRR-interval data set) from said subject during a stage of graduallyincreasing exercise load and gradually increasing heart rate;

(b) collecting a second RR-interval data set (e.g., a second QT- andRR-interval data set) from said subject during a stage of graduallydecreasing exercise load and gradually decreasing heart rate;

(c) comparing the first RR-interval data set to the second RR-intervaldata set to determine the difference between said data sets; and

(d) generating from said comparison of step (c) a measure of cardiacischemia during exercise in said subject, wherein a greater differencebetween said first and second data sets indicates greater cardiacischemia and lesser cardiovascular health in said subject.

In another embodiment of the invention, a rest stage following an abruptstop in exercise can serve as the period of gradually decreasing heartrate in a patient afflicted with coronary artery disease.

A second aspect of the present invention is a system for assessingcardiac ischemia in a subject to provide a measure of cardiovascularhealth in that subject. The system comprises:

(a) an ECG recorder for collecting a first RR-interval data set (e.g., afirst QT- and RR-interval data set) from the subject during a stage ofgradually increasing heart rate and collecting a second RR-interval dataset (e.g., a second QT- and RR-interval data) set from the subjectduring a stage of gradually decreasing heart rate;

(b) a computer program running in a computer or other suitable means forcomparing said first interval data set to the second interval data setto determine the difference between the data sets; and

(c) a computer program running in a computer or other suitable means forgenerating from said determination of the difference between the datasets a measure of cardiac ischemia during exercise in said subject,wherein a greater difference between the first and second data setsindicates greater cardiac ischemia and lesser cardiovascular health inthe subject.

A further aspect of the present invention is a method of assessingcardiac ischemia in a subject to provide a measure of cardiac orcardiovascular health in that subject, the method comprising the steps,performed on a computer system, of:

(a) providing a first RR-interval data set (e.g., a first QT- andRR-interval data set) collected from the subject during a stage ofgradually increasing heart rate;

(b) providing a second RR-interval data set (e.g., a second QT- andRR-interval data set) collected from the subject during a stage ofgradually decreasing heart rate;

(c) comparing the first interval data set to the second interval dataset to determine the difference between the data sets; and

(d) generating from the comparison of step (c) a measure of cardiacischemia during stimulation in the subject, wherein a greater differencebetween the first and second data sets indicates greater cardiacischemia and lesser cardiac or cardiovascular health in the subject.

The first and second interval data sets may be collected whileminimizing the influence of rapid transients due to autonomic nervoussystem and hormonal control on the data sets. The first and secondinterval data sets are collected without an intervening rest stage. Thegenerating step may be carried out by generating curves from each of thedata sets, and/or the generating step may be carried out by comparingthe shapes of the curves from data sets. In a particular embodiment, thegenerating step is carried out by determining a measure of the domainbetween the curves. In another particular embodiment, the generatingstep is carried out by both comparing the shapes of the curves from datasets and determining a measure of the domain between the curves. Themethod may include the further step of displaying the curves. In oneembodiment the comparing step may be carried out by: (i) filtering thefirst and second interval data sets; (ii) generating a smoothedhysteresis loop from the filtered first and second interval data sets;and then (iii) determining a measure of the domain inside the smoothedhysteresis loop. In another embodiment, the comparing step may becarried out by: (i) filtering the first and second interval data sets;(ii) generating preliminary minimal values for the first and secondinterval data sets; (iii) correcting the preliminary minimal values;(iv) generating first and second preliminary smoothed curves from eachof the filtered data sets; (v) correcting the preliminary smoothedcurves; (vi) fitting the preliminary smoothed curves; (vii) generating asmoothed hysteresis loop from the first and second fitted smoothedcurves; and then (viii) determining a measure of the domain inside thehysteresis loop. In still another embodiment, the comparing step iscarried out by: (i) filtering the first and second interval data sets bymoving average smoothing; (ii) generating a smoothed hysteresis loopfrom the filtered first and second interval data sets; and then (iii)determining a measure of the domain inside the hysteresis loop.

A further aspect of the present invention is a computer system forassessing cardiac ischemia in a subject to provide a measure of cardiacor cardiovascular health in that subject, the system comprising:

(a) means for providing a first RR-interval data set (e.g., a first QT-and RR-interval data set) from the subject during a stage of graduallyincreasing heart rate;

(b) means for providing a second RR-interval data set (e.g. a second QT-and RR-interval data set) from the subject during a stage of graduallydecreasing heart rate;

(c) means for comparing the first interval data set to the secondinterval data set to determine the difference between the data sets; and

(d) means for generating from the comparison of step (c) a measure ofcardiac ischemia during stimulation in the subject, wherein a greaterdifference between the first and second data sets indicates greatercardiac ischemia and lesser cardiac or cardiovascular health in thesubject.

A still further aspect of the present invention is a computer programproduct for assessing cardiac ischemia in a subject to provide a measureof cardiac or cardiovascular health in that subject, the computerprogram product comprising a computer usable storage medium havingcomputer readable program code means embodied in the medium, thecomputer readable program code means comprising:

(a) computer readable program code means for comparing a firstRR-interval data set (e.g., a first QT- and RR-interval data set) to asecond RR-interval data set (e.g., a second QT- and RR-interval dataset) to determine the difference between the data sets; and

(b) computer readable program code means for generating from thecomparison of step (c) a measure of cardiac ischemia during stimulationin the subject, wherein a greater difference between the first andsecond data sets indicates greater cardiac ischemia and lesser cardiacor cardiovascular health in the subject.

While the present invention is described herein primarily with referenceto the use of QT- and RR-interval data sets, it will be appreciated thatthe invention may be implemented in simplified form with the use ofRR-interval data sets alone. For use in the claims below, it will beunderstood that the term “RR-interval data set” is intended to beinclusive of both the embodiments of QT- and RR-interval data sets andRR-interval data sets alone, unless expressly subject to the provisothat the data set does not include a QT-interval data set.

The present invention is explained in greater detail in the drawingsherein and the specification set forth below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic graphic representation of the action potential incardiac muscle summed up over its volume and the inducedelectrocardiogram (ECG) recorded on a human's body surface.

FIG. 2A depicts the equations used in a simplified mathematical model ofperiodic excitation.

FIG. 2B depicts a periodic excitation wave (action potential, u, andinstantaneous threshold, v, generated by computer using a simplifiedmathematical model, the equations of which are set forth in FIG. 2A.

FIG. 2C depicts a family of four composite dispersion-restitution curvescorresponding to four values of the medium excitation threshold.

FIG. 3 is a block diagram of an apparatus for carrying out the presentmethod.

FIG. 4A is a block diagram of the processing steps for data acquisitionand analysis of the present invention.

FIG. 4B is an alternative block diagram of the processing steps for dataacquisition and analysis of the present invention.

FIG. 5 illustrates experimental QT-interval versus RR-intervalhysteresis loops for two healthy male (23year old, thick line and 47year old, thin line) subjects plotted on the compositedispersion-restitution curve plane.

FIG. 6 provides examples of the QT-RR interval hysteresis for two malesubjects, one with a conventional ECG ST-segment depression (thin line)and one with a history of a myocardial infarction 12 years prior to thetest (thick line). The generation of the curves is explained in greaterdetail in the specification below.

FIG. 7 illustrates sensitivity of the present invention and shows twoQT-RR interval hysteresis loops for a male subject, the first one (thicklines) corresponds to the initial test during which an ST-segmentdepression on a conventional ECG was observed, and the second one shownby thin lines measured after a period of regular exercise.

FIG. 8 illustrates a comparative cardiac ischemia analysis based on aparticular example of a normalized measure of the hysteresis loop area.<CII>=(CII−CII_(min))/(CII_(max)−CII_(min)) (“CII” means “cardiacischemia index”). O_(I), X_(I), and Y_(I) represent human subject data.X_(i) represents data collected from one subject (0.28-0.35) in a seriesof tests (day/night testing, run/walk, about two months between tests);exercise peak heart rate ranged from 120 to 135. Y_(i) represents datacollected from one subject (0.46-0.86) in a series of tests (run/walk,six weeks between tests before and after a period of regular exercisestage); exercise peak heart rate ranged from 122 to 146. Black barsindicate a zone (<CII> less than 0.70) in which a conventional STdepression method does not detect cardiac ischemia. The conventionalmethod may detect cardiac ischemia only in a significantly narrowerrange indicated by high white bars (Y₂, Y₃, O₇: <CII> greater than0.70).

FIG. 9 illustrates a typical rapid peripheral nervous system andhormonal control adjustment of the QT and RR interval to an abrupt stopin exercise (that is, an abrupt initiation of a rest stage).

FIG. 10 illustrates a typical slow (quasi-stationary) QT and RR intervaladjustment measured during gradually increasing and gradually decreasingcardiac stimulation.

FIG. 11 demonstrates a block-diagram of the data processing by themethod of optimized consolidation of a moving average, exponential andpolynomial fitting (Example 10, steps 1-8).

FIG. 12 demonstrates results of the processing throughout steps 1 to 8of Example 10. Upper panels show QT and RR data sets processed fromsteps 1 to 3 (from left to right respectively), and the QT/RR hysteresisloop after step 1. The exponential fitting curves (step 3) are shown ingray in the first two panels. Low panels show the same smoothdependencies after processing from step 4 to a final step 8. Here theCII (see right low panel) is equal to a ratio S/{((T_(RR)⁻(t_(end)−t_(min) ^(RR))−T_(RR) ⁻(0))((T_(QT) ⁺(t_(start)−t_(min)^(QT))−T_(QT) ⁺(0))}(see example 10, section 7).

FIG. 13 demonstrates a block-diagram of the data processing by themethod of a sequential moving average (Example 11, steps 1-3)

FIG. 14 demonstrates results of the processing throughout steps 1 to 2of Example 11. Upper panels show processed QT and RR data sets, and theQT/RR hysteresis loop after step 1 (from left to right respectively).Low panels show the same smooth dependencies after the second movingaverage processing and a final step 3.

FIG. 15 shows a general data flow chart for major steps in optimizednonlinear transformation method. The left-hand side and the right-handside boxes describe similar processing stages for the RR andQT-intervals, respectively.

FIG. 16 shows a detailed data flow chart for one data subset,{t^(k),T^(k) _(RR)} or {t^(k),T^(k) _(QT)} during stages (1a/b) through(3a/b) in FIG. 15. The preliminary stage, boxes 1 through 7, uses acombination of traditional data processing methods and includes: movingaveraging (1), determination of a minimum region (2), fitting aquadratic parabola to the data in this region (3), checking consistencyof the result (4), finding the minimum and centering data at the minimum(5) and (6), conditionally sorting the data (7). Stages (8) through (11)are based on the dual-nonlinear transformation method for the non-linearregression.

FIG. 17 displays the nonlinear transformation of a filtered RR-intervaldata set. Panel A shows the data on the original (t,y)-plane, theminimum is marked with an asterisk inside a circle. Panels B and C showthe transformed sets on the (t,u)-plane, for j=1 and for j=2,respectively. The image of the minimum is also marked with an encircledasterisk. Note that the transformed data sets concentrate around amonotonously growing (average) curve with a clearly linear portion inthe middle.

FIG. 18 is similar to FIG. 17 but for a QT-interval data set.

FIG. 19 displays an appropriately scaled representation for the familyof functions ξ(α,β,τ) for fifteen values of parameter β varying with thestep Δβ=0.1 from β=−0.9 (lower curve) through β=0 (medium, bold curve),to β=0.5 (upper curve). The function ξ(α,β,τ) is continuous in all threevariables and as a function of τ has a unit slope at τ=0, ξ′(α,β,0)=1.

FIG. 20 shows an example of full processing of the RR and QT data setsfor one patient. Panels A and C represent RR and QT data sets and theirfit. Panel B shows the corresponding ascending and descending curves andclosing line on the (T_(RR),T_(QT))-plane, on which the area of such ahysteresis loop has the dimension of time-squared. Panel D shows ahysteresis loop on the (f_(RR),T_(QT))-plane, where f_(RR)=1/T_(RR) isthe heart rate, on which the loop area is dimensionless. The totalerror-for Panel A is 2.2% and for Panel C is 0.8%

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention is explained in greater detail below. Thisdescription is not intended to be a detailed catalog of all thedifferent manners in which particular elements of the invention can beimplemented, and numerous variations will be apparent to those skilledin the art based upon the instant disclosure.

As will be appreciated by one of skill in the art, certain aspects ofthe present invention may be embodied as a method, data processingsystem, or computer program product. Accordingly, certain aspects of thepresent invention may take the form of an entirely hardware embodiment,an entirely software embodiment, or an embodiment combining software andhardware aspects. Furthermore, certain aspects of the present inventionmay take the form of a computer program product on a computer-usablestorage medium having computer readable program code means embodied inthe medium. Any suitable computer readable medium may be utilizedincluding, but not limited to, hard disks, CD-ROMs, optical storagedevices, and magnetic storage devices.

Certain aspects of the present invention are described below withreference to flowchart illustrations of methods, apparatus (systems),and computer program products. It will be understood that each block ofthe flowchart illustrations, and combinations of blocks in the flowchartillustrations, can be implemented by computer program instructions.These computer program instructions may be provided to a processor of ageneral purpose computer, special purpose computer, or otherprogrammable data processing apparatus to produce a machine, such thatthe instructions, which execute via the processor of the computer orother programmable data processing apparatus, create means forimplementing the functions specified in the flowchart block or blocks.

Computer program instructions may also be stored in a computer-readablememory that can direct a computer or other programmable data processingapparatus to function in a particular manner, such that the instructionsstored in the computer-readable memory produce an article of manufactureincluding instruction means which implement the function specified inthe flowchart block or blocks.

Computer program instructions may also be loaded onto a computer orother programmable data processing apparatus to cause a series ofoperational steps to be performed on the computer or other programmableapparatus to produce a computer implemented process such that theinstructions which execute on the computer or other programmableapparatus provide steps for implementing the functions specified in theflowchart block or blocks.

1. Definitions.

“Cardiac ischemia” refers to a lack of or insufficient blood supply toan area of cardiac muscle. Cardiac ischemia usually occurs in thepresence of arteriosclerotic occlusion of a single or a group ofcoronary arteries. Arteriosclerosis is a product of a lipid depositionprocess resulting in fibro-fatty accumulations, or plaques, which growon the internal walls of coronary arteries. Such an occlusioncompromises blood flow through the artery, which reduction then impairsoxygen supply to the surrounding tissues during increased physiologicalneed—for instance, during increased exercise loads. In the later stagesof cardiac ischemia (e.g. significant coronary artery occlusion), theblood supply may be insufficient even while the cardiac muscle is atrest. However, in its earlier stages such ischemia is reversible in amanner analogous to how the cardiac muscle is restored to normalfunction when the oxygen supply to it returns to a normal physiologicallevel. Thus, ischemia that may be detected by the present inventionincludes episodic, chronic and acute ischemia.

“Exercise” as used herein refers to voluntary skeletal muscle activityof a subject that increases heart rate above that found at a sustainedstationary resting state. Examples of exercise include, but are notlimited to, cycling, rowing, weight-lifting, walking, running,stair-stepping, etc., which may be implemented on a stationary devicesuch as a treadmill or in a non-stationary environment.

“Exercise load” or “load level” refers to the relative strenuousness ofa particular exercise, with greater loads or load levels for a givenexercise producing a greater heart rate in a subject. For example, loadmay be increased in weight-lifting by increasing the amount of weight;load may be increased in walking or running by increasing the speedand/or increasing the slope or incline of the walking or runningsurface; etc.

“Gradually increasing” and “gradually decreasing” an exercise loadrefers to exercise in which the subject is caused to perform an exerciseunder a plurality of different sequentially increasing or sequentiallydecreasing loads. The number of steps in the sequence can be infinite sothe terms gradually increasing and gradually decreasing loads includecontinuous load increase and decrease, respectively.

“Intervening rest”, when used to refer to a stage following increasedcardiac stimulation, refers to a stage of time initiated by asufficiently abrupt decrease in heart stimulation (e.g., an abruptdecrease in exercise load) so that it evokes a clear sympatho-adrenalresponse. Thus, an intervening rest stage is characterized by a rapidsympatho-adrenal adjustment (as further described in Example 8 below),and the inclusion of an intervening rest stage precludes the use of aquasi-stationary exercise (or stimulation) protocol (as furtherdescribed in Example 9 below).

“Hysteresis” refers to a lagging of the physiological effect when theexternal conditions are changed.

“Hysteresis curves” refer to a pair of curves in which one curvereflects the response of a system to a first sequence of conditions,such as gradually increasing heart rate, and the other curve reflectsthe response of a system to a second sequence of conditions, such asgradually decreasing heart rate. Here both sets of conditions areessentially the same—i.e., consist of the same (or approximately thesame) steps—but are passed in different order in the course of time. A“hysteresis loop” refers to a loop formed by the two contiguous curvesof the pair.

“Electrocardiogram” or “ECG” refers to a continuous or sequential record(or a set of such records) of a local electrical potential fieldobtained from one or more locations outside the cardiac muscle. Thisfield is generated by the combined electrical activity (action potentialgeneration) of multiple cardiac cells. The recording electrodes may beeither subcutaneously implanted or may be temporarily attached to thesurface of the skin of the subject, usually in the thoracic region. AnECG record typically includes the single-lead ECG signal that representsa potential difference between any two of the recording sites includingthe site with a zero or ground potential.

“Quasi-stationary conditions” refer to a gradual change in the externalconditions and/or the physiological response it causes that occurs muchslower than any corresponding adjustment due tosympathetic/parasympathetic and hormonal control. If the representativetime of the external conditions variation is denoted by τ_(ext), andτ_(int) is a representative time of the fastest of the internal,sympathetic/parasympathetic and hormonal control, then “quasi-stationaryconditions” indicates τ_(ext)>>τ_(int) (e.g., τ_(ext) is at least aboutfive times greater than τ_(int)). “An abrupt change” refers to anopposite situation corresponding to a sufficiently fast change in theexternal conditions as compared with the ratesympathetic/parasympathetic and hormonal control—that is, it requiresthat τ_(ext)<<τ_(int) (e.g., τ_(ext) is at least about five times lessthan τ_(int)). In particular, “an abrupt stop” refers to a fast removalof the exercise load that occurs during time shorter than τ_(int)˜20 or30 seconds (see FIG. 9 below and comments therein).

“QT- and RR-data set” refers to a record of the time course of anelectrical signal comprising action potentials spreading through cardiacmuscle. Any single lead ECG record incorporates a group of threeconsecutive sharp deflections usually called a QRS complex and generatedby the propagation of the action potential's front through theventricles. In contrast, the electrical recovery of ventricular tissueis seen on the ECG as a relatively small deflection known as the T wave.The time interval between the cardiac cycles (i.e., between the maximaof the consecutive R-waves) is called an RR-interval, while the actionpotential duration (i.e., the time between the beginning of a QRScomplex and the end of the ensuing T-wave) is called a QT-interval.Alternative definitions of these intervals can be equivalently used inthe framework of the present invention. For example, an RR-interval canbe defined as the time between any two similar points, such as thesimilar inflection points, on two consecutive R-waves, or any other wayto measure cardiac cycle length. A QT-interval can be defined as thetime interval between the peak of the Q-wave and the peak of the T wave.It can also be defined as the time interval between the beginning (orthe center) of the Q-wave and the end of the ensuing T-wave defined asthe point on the time axis (the base line) at which it intersects withthe linear extrapolation of the T-wave's falling branch and started fromits inflection point, or any other way to measure action potentialduration. An ordered set of such interval durations simultaneously withthe time instants of their beginnings or ends which are accumulated on abeat to beat basis or on any given beat sampling rate basis form acorresponding QT- and RR-interval data set. Thus, a QT- and RR-intervaldata set will contain two QT-interval related sequences {T_(QT,1),T_(QT,2), . . . , T_(QT,n),} and {t₁, t₂, . . . , t_(n)}, and will alsocontain two RR-interval related sequences {T_(RR,1), T_(RR,2), . . . ,T_(RR,n),} and {t₁, t₂, . . . , t_(n)} (the sequence {t₁, t₂, . . . ,t_(n)} may or may not exactly coincide with the similar sequence in theQT data set).

In the following definitions, C[a,b] shall denote a set of continuousfunctions f(t) on a segment [a,b]. {t_(i)}, i=1,2, . . . , N, denotes aset of points from [a,b], i.e. {t_(i)}={t_(i): a≦t_(i)≦b, i=1, 2, . . ., N} and {f(t_(i))}, where fεC[a,b], denotes a set of values of thefunction fat the points {t_(i)}. In matrix operations the quantitiesτ={t_(i)}, y={f(t_(i))}, are treated as column vectors. E_(N) shalldenote a N-dimensional metric space with the metric R_(N)(x,y),x,yεE_(N). (R_(N)(x,y) is said to be a distance between points x and y.)A (total) variation $\overset{b}{\underset{a}{V}}\lbrack F\rbrack$

is defined for any absolutely continuous function F from C[a,b] as theintegral (a Stieltjes integral) $\begin{matrix}{\left. {{\underset{a}{\overset{b}{V}}\left\lbrack {F(t)} \right\rbrack} \equiv \int\limits_{a}^{b}} \middle| {{F(t)}} \right| = {\int\limits_{a}^{b}\left| {F^{\prime}(t)} \middle| {{t}.} \right.}} & \text{(D.1)}\end{matrix}$

For a function F monotonic on segment [a,b] its variation is simply|F(a)-F(b)|. If a function F(t) has alternating maxima and minima, thenthe total variation of F is the sum of its variations on the intervalsof monotonicity. For example, if the points of minima and maxima arex₁=a, x₂, x₃, . . . , x_(k)=b then $\begin{matrix}{{\underset{a}{\overset{b}{V}}\left\lbrack {F(t)} \right\rbrack} = {\sum\limits_{i = 1}^{k - 1}\left| {{{F\left( x_{i} \right)} - {F\left( x_{i + 1} \right)}}\left| . \right.} \right.}} & \text{(D.2)}\end{matrix}$

Fitting (Best Fitting): Let {tilde over (C)}[a,b] be a subset of C[a,b].A continuous function f(t), fε{tilde over (C)}[a,b] is called the (best)fit (or the best fitting) function of class {tilde over (C)}[a,b] withrespect to metric R_(N) to a data set {x_(i),t_(i)} (i=1, 2, . . . , N}if $\begin{matrix}{{R_{N}\left( {\left\{ {f\left( t_{i} \right)} \right\},\left\{ x_{i} \right\}} \right)} = \min\limits_{f \in {\overset{\sim}{C}{\lbrack{a,b}\rbrack}}}} & \text{(D.3)}\end{matrix}$

The minimum value of R_(N) is then called the error of the fit. Thefunctions f(t) from {tilde over (C)}[a,b] will be called trialfunctions.

In most cases E_(N) is implied to be an Euclidean space with anEuclidean metric. The error R_(N) then becomes the familiarmean-root-square error. The fit is performed on a subset {tilde over(C)}[a,b] since it usually implies a specific parametrization of thetrial functions and/or such constrains as the requirements that thetrial functions pass through a given point and/or have a given value ofthe slope at a given point.

A Smoother Function (Comparison of Smoothness): Let f(t) and g(t) befunctions from C[a,b] that have absolutely continuous derivatives onthis segment. The function f(t) is smoother than the function g(t) if$\begin{matrix}{{{\underset{a}{\overset{b}{V}}\left\lbrack {f(t)} \right\rbrack} \leq {\underset{a}{\overset{b}{V}}\left\lbrack {g(t)} \right\rbrack}},{and}} & \text{(D.4)} \\{{{\underset{a}{\overset{b}{V}}\left\lbrack {f^{\prime}(t)} \right\rbrack} \leq {\underset{a}{\overset{b}{V}}\left\lbrack {g^{\prime}(t)} \right\rbrack}},} & \text{(D.5)}\end{matrix}$

where the prime denotes a time derivative, and a strict inequality holdsin at least one of relations (D.4) and (D.5).

A Smoother Set: A set {x_(i),t_(i)} (i=1, 2, . . . , N} is smoother thanthe set {x′_(j),t′_(j)} (j=1, 2, . . . , N′} if the former can be fitwith a smoother function f(t) of the same class within the same orsmaller error than the latter.

Smoothing of a Data Set: A (linear) transformation of a data set(x,t)≡{x_(i),t_(i)} (i=1, 2, . . . , N₀} into another set(y,τ)≡{y_(j),τ_(j)} (j=1, 2, . . . , N₁} of the form

y=A·x, τ=B·t,  (D.6)

where A and B are N₁×N₀ matrices, is called a smoothing if the latterset is smoother than the former. One can refer to {y_(j),τ_(j)} as asmoothed set

A Measure of a Closed Domain: Let Ω be a singly connected domain on theplane (τ,T) with the boundary formed by a simple (i.e., withoutself-intersections) continuous curve. A measure M of such a domain Ω onthe plane (τ,T) is defined as the Riemann integral $\begin{matrix}{M = {\int_{\Omega}{\int{{\rho \left( {\tau,T} \right)}{\tau}{T}}}}} & \text{(D.7)}\end{matrix}$

where ρ(τ,T) is a nonnegative (weight) function on Ω.

Note that when ρ(τ,T)≡1 the measure M of the domain coincides with itsarea, A; when ρ(τ,T)≡1/τ², the measure, M, has the meaning of the area,A′, of the domain Ω′ on the transformed plane (f,T), where f=1/τ can beunderstood as the heart rate since the quantity τ has the meaning ofRR-interval. [The domain Ω′ is the image of domain Ω under the mapping(τ,T)→(1/τ,T).]

2. Dispersion/Restitution Curves.

FIG. 1 illustrates the correspondence between the temporal phases of theperiodic action potential (AP, upper graph, 20) generated inside cardiacmuscle and summed up over its entire volume and the electrical signalproduced on the body surface and recorded as an electrocardiogram (ECG,lower graph, 21). The figure depicts two regular cardiac cycles. Duringthe upstroke of the action potential the QRS-complex is formed. Itconsists of three waves, Q, R, and S, which are marked on the lowerpanel. The recovery stage of the action potential is characterized byits fall off on the AP plot and by the T-wave on the ECG plot. One cansee that the action potential duration is well represented by the timebetween Q and T waves and is conventionally defined as the QT interval,measured from the beginning of the Q wave to the end of the following Twave. The time between consecutive R-waves (RR interval) represents theduration of a cardiac cycle, while its reciprocal value represents thecorresponding instantaneous heart rate.

FIG. 2 illustrates major aspects of the process of propagation of aperiodic action potential through cardiac tissue and the formation of acorresponding composite dispersion-restitution curve. The tissue can beconsidered as a continuous medium and the propagation process as arepetition at each medium point of the consecutive phases of excitationand recovery. The former phase is characterized by a fast growth of thelocal membrane potential (depolarization), and the latter by its returnto a negative resting value (repolarization). The excitation phaseinvolves a very fast (˜0.1 ms) decrease in the excitation threshold andthe following development of a fast inward sodium current that causesthe upstroke of the action potential (˜1 ms). Next, during anintermediate plateau phase (˜200 ms) sodium current is inactivated;calcium and potassium currents are developing while the membrane istemporarily unexcitable (i.e., the threshold is high). During the nextrecovery phase (˜100 ms), a potassium current repolarizes the membraneso it again becomes excitable (the excitation threshold is lowered).

The complicated description of a multitude of ionic currents involved inthe process can be circumvented if one treats the process directly interms of the local membrane potential, u, and a local excitationthreshold, v. Such a mathematical description referred to as the CSCmodel, was developed by Chernyak, Starobin, & Cohen (Phys. Rev. Lett.,80, pp.5675-5678, 1998) and is presented as a set of twoReaction-Diffusion (RD) equations in panel A. The left-hand side of thefirst equation describes local accumulation of the electric charge onthe membrane, the first term in the right-hand side describes Ohmiccoupling between neighboring points of the medium, and the term i(u,v)represents the transmembrane current as a function of the membranepotential and the varying excitation threshold (ε is a small constant,the ratio of the slow recovery rate to the fast excitation rate). Aperiodic solution (a wave-train) can be found analytically for someparticular functions i(u)v) and g(u,v). The wave-train shown in panel Bhas been calculated for g(u,v)=ζu+v_(r)−v, where ζ and v_(r) areappropriately chosen constants (v_(r) has the meaning of the initialexcitation threshold and is the main determinant of the mediumexcitability). The function i(u,v) was chosen to consist of two linearpieces, one for the sub-threshold region, u<v, and one forsupra-threshold region, u>v. That is i(u,v)=λ_(r)u when u≦v, andi(u,v)=λ_(ex)(u−u_(ex)) when u>v, where λ_(r) and λ_(ex) are membranechord conductances in the resting (u=0) and excited (u=u_(ex)) states,respectively. The resting state u=0 is taken as the origin of thepotential scale. We used such units that λ_(ex)=1 and u_(ex)=1. (Fordetails see Chernyak & Starobin, Critical Reviews in Biomed. Eng. 27,359-414 (1999)).

A medium with higher excitability, corresponding to the tissue withbetter conduction, gives rise to a faster, more robust action potentialwith a longer Action Potential Duration (APD). This condition also meansthat a longer-lasting excitation propagates faster. Similarly, a wavetrain with a higher frequency propagates slower since the medium hasless time to recover from the preceding excitation and thus has a lowereffective excitability. These are quite generic features that areincorporated in the CSC model. In physics, the relation between thewave's speed, c, and its frequency, f or its period, T=1/f, is called adispersion relation. In the CSC model the dispersion relation can beobtained in an explicit form T=F_(T)(c), where F_(T) is a known functionof c and the medium parameters. The CSC model also allows us to find arelation between the propagation speed and the APD, T_(AP), in theexplicit form T_(AP)=F_(AP)(c), which represents the restitutionproperties of the medium. In the medical literature, the restitutioncurve is T_(AP) versus diastolic interval T_(DI), which differentlymakes a quite similar physical statement. One can consider a pair ofdispersion and restitution relations {T=F_(T)(c),T_(AP)=F_(AP)(c)} as aparametric representation of a single curve on the (T,T_(AP))-plane asshown in panel C (FIG. 2). Such a curve (relation) shall be referred toas a composite dispersion-restitution curve (relation) and can bedirectly obtained from an experimental ECG recording by determining theQT-RR interval data set and plotting T_(QT) versus T_(RR). A conditionthat the experimental {T_(QT),T_(RR)} data set indeed represents thecomposite dispersion-restitution relation is the requirement that thedata are collected under quasi-stationary conditions. Understanding thisfact is a key discovery for the present invention.

3. Testing Methods.

The methods of the present invention are primarily intended for thetesting of human subjects. Virtually any human subject can be tested bythe methods of the present invention, including male, female, juvenile,adolescent, adult, and geriatric subjects. The methods may be carriedout as an initial screening test on subjects for which no substantialprevious history or record is available, or may be carried out on arepeated basis on the same subject (particularly where a comparativequantitative indicium of an individual's cardiac health over time isdesired) to assess the effect or influence of intervening events and/orintervening therapy on that subject between testing sessions.

As noted above, the method of the present invention generally comprises(a) collecting a first QT- and RR-interval data set from said subjectduring a stage of gradually increasing heart rate; (b) collecting asecond QT- and RR-interval data set from said subject during a stage ofgradually decreasing heart rate; (c) comparing said first QT- andRR-interval data set to said second QT- and RR-interval data set todetermine the difference between said data sets; and (d) generating fromsaid comparison of step (c) a measure of cardiac ischemia in thesubject. A greater difference between the first and second data setsindicates greater cardiac ischemia and lesser cardiac or cardiovascularhealth in that subject.

The stages of gradually increasing and gradually decreasing heart rateare carried out in a manner that maintains during both periodsessentially or substantially the same stimulation of the heart by theperipheral nervous and hormonal control systems, so that it is theeffect of cardiac ischemia rather than that of the external controlwhich is measured by means of the present invention. This methodologycan be carried out by a variety of techniques, with the technique ofconducting two consecutive stages of gradually increasing and graduallydecreasing exercise loads (or average heart rates) being currentlypreferred.

The stage of gradually increasing exercise load (or increased averageheart rate) and the stage of gradually decreasing exercise load (ordecreased average heart rate) may be the same in duration or may bedifferent in duration. In general, each stage is at least 3, 5, 8, or 10minutes or more in duration. Together, the duration of the two stagesmay be from about 6, 10, 16 or 20 minutes in duration to about 30, 40,or 60 minutes in duration or more. The two stages are preferably carriedout sequentially in time—that is, with one stage following after theother substantially immediately, without an intervening rest stage. Inthe alternative, the two stages may be carried out separately in time,with an intervening “plateau” stage (e.g., of from 1 to 5 minutes)during which cardiac stimulation or exercise load is held substantiallyconstant, before the stage of decreasing load is initiated. In aparticular embodiment discussed below, where the subject is afflictedwith coronary artery disease, a stage of gradually decreasing exerciseload may be considered to take place during the period following anabrupt stop in exercise.

The exercise protocol may include the same or different sets of loadsteps during the stages of increasing or decreasing heart rates. Forexample, the peak load in each stage may be the same or different, andthe minimum load in each stage may be the same or different. In general,each stage consists of at least two or three different load levels, inascending or descending order depending upon the stage. Relatively highload levels, which result in relatively high heart rates, can be usedbut are not essential. An advantage of the present invention is that itssensitivity allows both exercise procedures to be carried out atrelatively low load levels that do not unduly increase the pulse rate ofthe subject. For example, the method may be carried out so that theheart rate of the subject during either the ascending or descendingstage (or both) does not exceed about 140, 120, or even 100 beats perminute, depending upon the condition of the subject. Of course, datacollected at heart rates above 100, 120, or 140 beats per minute mayalso be utilized if desired, again depending upon the condition of thesubject.

For example, for an athletic or trained subject, for the first orascending stage, a first load level may be selected to require a poweroutput of 60 to 100 or 150 watts by the subject; an intermediate loadlevel may be selected to require a power output of 100 to 150 or 200watts by the subject; and a third load level may be selected to requirea power output of 200 to 300 or 450 watts or more by the subject. Forthe second or descending stage, a first load level may be selected torequire a power output of 200 to 300 or 450 watts or more by thesubject; an intermediate or second load level may be selected to requirea power output of 100 to 150 or 200 watts by the subject; and a thirdload level may be selected to require a power output of 60 to 100 or 150watts by the subject. Additional load levels may be included before,after, or between all of the foregoing load levels as desired, andadjustment between load levels can be carried out in any suitablemanner, including step-wise or continuously.

In a farther example, for an average subject or a subject with a historyof cardiovascular disease, for the first or ascending stage, a firstload level may be selected to require a power output of 40 to 75 or 100watts by the subject; an intermediate load level may be selected torequire a power output of 75 to 100 or 150 watts by the subject; and athird load level may be selected to require a power output of 125 to 200or 300 watts or more by the subject. For the second or descending stage,a first load level may be selected to require a power output of 125 to200 or 300 watts or more by the subject; an intermediate or second loadlevel may be selected to require a power output of 75 to 100 or 150watts by the subject; and a third load level may be selected to requirea power output of 40 to 75 or 100 watts by the subject. As before,additional load levels may be included before, after, or between all ofthe foregoing load levels as desired, and adjustment between load levelscan be carried out in any suitable manner, including step-wise orcontinuously.

The heart rate may be gradually increased and gradually decreased bysubjecting the patient to a predetermined schedule of stimulation. Forexample, the patient may be subjected to a gradually increasing exerciseload and gradually decreasing exercise load, or gradually increasingelectrical or pharmacological stimulation and gradually decreasingelectrical or pharmacological stimulation, according to a predeterminedprogram or schedule. Such a predetermined schedule is without feedbackof actual heart rate from the patient. In the alternative, the heartrate of the patient may be gradually increased and gradually decreasedin response to actual heart rate data collected from concurrentmonitoring of said patient. Such a system is a feedback system. Forexample, the heart rate of the patient may be monitored during the testand the exercise load (speed and/or incline, in the case of a treadmill)can be adjusted so that the heart rate varies in a prescribed way duringboth stages of the test. The monitoring and control of the load can beaccomplished by a computer or other control system using a simplecontrol program and an output panel connected to the control system andto the exercise device that generates an analog signal to the exercisedevice. One advantage of such a feedback system is that (if desired) thecontrol system can insure that the heart rate increases substantiallylinearly during the first stage and decreases substantially linearlyduring the second stage.

The generating step (d) may be carried out by any suitable means, suchas by generating curves from the data sets (with or without actuallydisplaying the curves), and then (i) directly or indirectly evaluating ameasure (e.g., as defined in the integral theory) of the domain (e.g.,area) between the hysteresis curves, a greater measure indicatinggreater cardiac ischemia in said subject, (ii) directly or indirectlycomparing the shapes (e.g., slopes or derivatives thereof) of thecurves, with a greater difference in shape indicating greater cardiacischemia in the subject; or (iii) combinations of (i) and (ii). Specificexamples are given in Example 4 below.

The method of the invention may further comprise the steps of (e)comparing the measure of cardiac ischemia during exercise to at leastone reference value (e.g., a mean, median or mode for the quantitativeindicia from a population or subpopulation of individuals) and then (F)generating from the comparison of step (e) at least one quantitativeindicium of cardiovascular health for said subject. Any suchquantitative indicium may be generated on a one-time basis (e.g., forassessing the likelihood that the subject is at risk to experience afuture ischemia-related cardiac incident such as myocardial infarctionor ventricular tachycardia), or may be generated to monitor the progressof the subject over time, either in response to a particular prescribedcardiovascular therapy, or simply as an ongoing monitoring of thephysical condition of the subject for improvement or decline (again,specific examples are given in Example 4 below). In such a case, steps(a) through (f) above are repeated on at least one separate occasion toassess the efficacy of the cardiovascular therapy or the progress of thesubject. A decrease in the difference between said data sets from beforesaid therapy to after said therapy, or over time, indicates animprovement in cardiac health in said subject from said cardiovasculartherapy. Any suitable cardiovascular therapy can be administered,including but not limited to, aerobic exercise, muscle strengthbuilding, change in diet, nutritional supplement, weight loss, smokingcessation, stress reduction, pharmaceutical treatment (including genetherapy), surgical treatment (including both open heart and closed heartprocedures such as bypass, balloon angioplasty, catheter ablation, etc.)and combinations thereof.

The therapy or therapeutic intervention may be one that is approved orone that is experimental. In the latter case, the present invention maybe implemented in the context of a clinical trial of the experimentaltherapy, with testing being carried out before and after therapy (and/orduring therapy) as an aid in determining the efficacy of the proposedtherapy.

4. Testing Apparatus.

FIG. 3 provides an example of the apparatus for data acquisition,processing and analysis by the present invention. Electrocardiograms arerecorded by an ECG recorder 30, via electrical leads placed on asubject's body. The ECG recorder may be, for example, a standardmulti-lead Holter recorder or any other appropriate recorder. Theanalog/digital converter 31 digitizes the signals recorded by the ECGrecorder and transfers them to a personal computer 32, or other computeror central processing unit, through a standard external input/outputport. The digitized ECG data can then be processed by standardcomputer-based waveform analyzer software. Compositedispersion-restitution curves and a cardiac or cardiovascular healthindicium or other quantitative measure of the presence, absence ordegree of cardiac ischemia can then be calculated automatically in thecomputer through a program (e.g., Basic, Fortran, C++, etc.) implementedtherein as software, hardware, or both hardware and software.

FIG. 4A and FIG. 4B illustrate the major steps of digitized dataprocessing in order to generate an analysis of a QT-RR data setcollected from a subject during there-and-back quasi-stationary changesin physiological conditions. The first four steps in FIG. 4A and FIG. 4Bare substantially the same. The digitized data collected from amulti-lead recorder are stored in a computer memory for each lead as adata array 40 a, 40 b. The size of each data array is determined by thedurations of the ascending and descending heart rate stages and asampling rate used by the waveform analyzer, which processes an incomingdigitized ECG signal. The waveform analyzer software first detects majorcharacteristic waves (Q,R,S and T waves) of the ECG signal in eachparticular lead 41 a, 41 b. Then in each ECG lead it determines the timeintervals between consecutive R waves and the beginning of Q and the endof T waves 42 a, 42 b. Using these reference points it calculates heartrate and RR- and QT-intervals. Then, the application part of thesoftware sorts the intervals for the ascending and descending heart ratestages 43 a, 43 b. The next two steps can be made in one of the twoalternative ways shown in FIGS. 4A and 4B, respectively. The fifth stepas shown in FIG. 4A consists of displaying by the application part ofsoftware QT-intervals versus RR-intervals 44 a, separately for theascending and descending heart rate stages effected by there-and-backgradual changes in physiological conditions such as exercise,pharmacological/electrical stimulation, etc. The same part of thesoftware performs the next step 45 a, which is smoothing, filtering ordata fitting, using exponential or any other suitable functions, inorder to obtain a sufficiently smooth curve T_(QT)=F(T_(RR)) for eachstage. An alternative for the last two steps shown in FIG. 4B requiresthat the application part of the software first averages, and/or filtersand/or fits, using exponential or any other suitable functions, the QTintervals as functions of time for both stages and similarly processesthe RR-interval data set to produce two sufficiently smooth curvesT_(QT)=F_(QT)(t) and T_(RR)=F_(RR)(t), each including the ascending anddescending heart rate branches 44 b. At the next step 45 b theapplication part of the software uses this parametric representation toeliminate time and generate and plot a sufficiently smooth hysteresisloop T_(QT)=F(T_(RR)). The following steps shown in FIGS. 4A and FIG. 4Bare again substantially the same. The next step 46 a, 46 b performed bythe application part of the software can be graphically presented asclosing the two branch hysteresis loop with an appropriateinterconnecting or partially connecting line, such as a verticalstraight line or a line connecting the initial and final points, inorder to produce a closed hysteresis loop on the (T_(QT), T_(RR))-plane.At the next step 47 a, 47 b the application software evaluates for eachECG lead an appropriate measure of the domain inside the closedhysteresis loop. A measure, as defined in mathematical integral theory,is a generalization of the concept of an area and may includeappropriate weight functions increasing or decreasing the contributionof different portions of the domain into said measure. The final step 48a, 48 b of the data processing for each ECG lead is that the applicationsoftware calculates indexes by appropriately renormalizing the saidmeasure or any monotonous functions of said measure. The measure itselfalong with the indexes may reflect both the severity of theexercise-induced ischemia, as well as a predisposition to local ischemiathat can be reflected in some particularities of the shape of themeasured composite dispersion-restitution curves. The results of allabove-mentioned signal processing steps may be used to quantitativelyassess cardiac ischemia and, as a simultaneous option, cardiovascularsystem health of a particular individual under test.

Instead of using the (T_(QT),T_(RR))-plane a similar data processingprocedure can equivalently be performed on any plane obtained by anon-degenerate transformation of the (T_(QT),T_(RR))-plane, such as(T_(QT),f_(RR)) where f_(RR)=1/T_(RR) is the heart rate or the like.Such a transformation can be partly or fully incorporated in theappropriate definition of the said measure.

5. Conditions Under Which an Abrupt Stop Exercise Protocol can beConsidered as a Quasi-Stationary Protocol.

In general, each stage of gradually increasing and decreasingquasi-stationary exercise protocol is at least 3, 5, 8, or 10 minutes induration. Each stage's duration is approximately an order of magnitudelonger than the average duration (1 minute) of heart rate (HR)adjustment during an abrupt stop of the exercise between average peakload rate (˜120-150 beat/min) and average rest (˜50-70 beat/min) heartrate values.

One should note that the ˜1 minute HR adjustment period after an abruptstop of exercise is typical only for healthy individuals and those withnot more than a relatively moderate level of coronary artery disease.However, due to rapid development of massive exercise-induced ischemiafor individuals with a pronounced coronary artery disease level the sameadjustment period can be significantly longer—up to 10 minutes or morein duration. In these cases the HR deviations (described in the example9 below) are small and indicate that such an ill patient remains under asignificant physical stress even after an abrupt stop of exercise,without further exercise load exposure. In such cases a physician mustusually interrupt the protocol prior to completion of a fullquasi-stationary exercise regimen. However, under these conditions arecovery portion of the QT/RR hysteresis loop, as well as a loop formedafter an abrupt stop of exercise, can be considered as thequasi-stationary loop. Indeed, a slow heart rate recovery to a levelequal to HR prior to the exercise takes 3, 5, 8, 10 or more minutes induration with small HR deviations and, therefore, still satisfies theunderlying definition of a gradual exercise protocol (see example 9,below).

Thus, for ill patients afflicted with coronary artery disease, an abruptstop of exercise does not prevent the completion of the method of thepresent invention, since due to a prolonged HR recovery stage anindicium of cardiac or cardiovascular health can still be calculated asa quasi-stationary loop index without a completion of a full exerciseprotocol.

Note that typically a patient with a distinguished coronary arterydisease level, as determined by physical exhaustion, shortness ofbreath, chest pain, and/or some other clinical symptom, is unable toexercise longer than 3, 5, 8 or 10 or more minutes at even a low-levelpower output of about 20 watts. A gradual recovery process followed theabrupt stop of such exercise in such patients satisfies the definitionof a quasi-stationary process as given herein (see, e.g., Example 9).Note that patients with moderate levels of coronary artery disease canexercise longer, up to 20 minutes or more, and may be exposed tosignificantly higher exercise workouts ranging from 50 to 300 watts.

The present invention is explained in greater detail in the non-limitingexamples set forth below.

EXAMPLE 1 Testing Apparatus

A testing apparatus consistent with FIG. 3 was assembled. Theelectrocardiograms are recorded by an RZ152PM12 Digital ECG HolterRecorder (ROZINN ELECTRONICS, INC.; 71-22 Myrtle Av., Glendale, N.Y.,USA 11385-7254), via 12 electrical leads with Lead-Lok Holter/StressTest Electrodes LL510 (LEAD-LOK, INC.; 500 Airport Way, P.O. Box L,Sandpoint, Id., USA 83864) placed on a subject's body in accordance withthe manufacturer's instructions. Digital ECG data are transferred to apersonal computer (Dell Dimension XPS T500 MHz/Windows 98) using a 40 MBflash card (RZFC40) with a PC 700 flash card reader, both from RozinnElectronics, Inc. Holter for Windows (4.0.25) waveform analysis softwareis installed in the computer, which is used to process data by astandard computer based waveform analyzer software. Compositedispersion-restitution curves and an indicium that provides aquantitative characteristic of the extent of cardiac ischemia are thencalculated manually or automatically in the computer through a programimplemented in Fortran 90.

Experimental data were collected during an exercise protocol programmedin a Landice L7 Executive Treadmill (Landice Treadmills; 111 CanfieldAv., Randolph, N.J. 07869). The programmed protocol included 20step-wise intervals of a constant exercise load from 48 seconds to 1.5minutes each in duration. Altogether these intervals formed twoequal-in-duration gradually increasing and gradually decreasing exerciseload stages, with total duration varying from 16 to 30 minutes. For eachstage a treadmill belt speed and elevation varied there-and-back,depending on the subject's age and health conditions, from 1.5 miles perhour to 5.5 miles per hour and from one to ten degrees of treadmillelevation, respectively.

EXAMPLES 2-6 Human Hysteresis Curve Studies

These examples illustrate quasi-stationary ischemia-induced QT-RRinterval hystereses in a variety of different human subjects. These datademonstrate a high sensitivity and the high resolution of the method.

EXAMPLES 2-3 Hysteresis Curves in Healthy Male Subjects of DifferentAges

These examples were carried out on two male subjects with an apparatusand procedure as described in Example 1 above. Referring to FIG. 5, onecan readily see a significant difference in areas of hystereses betweentwo generally healthy male subjects of different ages. These subjects(23 and 47 years old) exercised on a treadmill according to aquasi-stationary 30-minute protocol with gradually increasing andgradually decreasing exercise load. Here squares and circles (thickline) indicate a hysteresis loop for the 23 year old subject, anddiamonds and triangles (thin line) correspond to a larger loop for the47 year old subject. Fitting curves are obtained using the third-orderpolynomial functions. A beat sampling rate with which a waveformanalyzer determines QT and RR intervals is equal to one sample perminute. Neither of the subjects had a conventional ischemia-induceddepression of the ECG-ST segments. However, the method of the presentinvention allows one to observe ischemia-induced hystereses that providea satisfactory resolution within a conventionally sub-threshold range ofischemic events and allows one to quantitatively differentiate betweenthe hystereses of the two subjects.

EXAMPLES 4-5 Hysteresis Curves for Subjects with ST Segment Depressionor Prior Cardiac Infarction

These examples were carried out on two 55-year-old male subjects with anapparatus and procedure as described in Example 1 above. FIG. 6illustrates quasi-stationary QT-RR interval hystereses for the malesubjects. The curves fitted to the squares and empty circles relate tothe first individual and illustrate a case of cardiac ischemia alsodetectable by the conventional ECG-ST segment depression technique. Thecurves fitted to the diamonds and triangles relate to the other subject,an individual who previously had experienced a myocardial infarction.These subjects exercised on a treadmill according to a quasi-stationary20-minute protocol with a gradually increasing and gradually decreasingexercise load. Fitting curves are obtained using third-order polynomialfunctions. These cases demonstrate that the method of the presentinvention allows one to resolve and quantitatively characterize thedifference between (1) levels of ischemia that can be detected by theconventional ST depression method, and (2) low levels of ischemia(illustrated in FIG. 5) that are subthreshold for the conventionalmethod and therefore undetectable by it. The levels of exercise-inducedischemia reported in FIG. 5 are significantly lower than those shown inFIG. 6. This fact illustrates insufficient resolution of a conventionalST depression method in comparison with the method of the presentinvention.

EXAMPLE 6 Hysteresis Curves in the Same Subject Before and After aRegular Exercise Regimen

This example was carried out with an apparatus and procedure asdescribed in Example 1 above. FIG. 7 provides examples ofquasi-stationary hystereses for a 55 year-old male subject before andafter he engaged in a practice of regular aerobic exercise. Bothexperiments were performed according to the same quasi-stationary20-minute protocol with a gradually increasing and gradually decreasingexercise load. Fitting curves are obtained using third-order polynomialfunctions. The first test shows a pronounced exercise-induced cardiacischemic event developed near the peak level of exercise load, detectedby both the method of the present invention and a conventional ECG-STdepression method. The maximum heart rate reached during the first test(before a regular exercise regimen was undertaken) was equal to 146.After a course of regular exercise the subject improved hiscardiovascular health, which can be conventionally roughly,qualitatively, estimated by a comparison of peak heart rates. Indeed,the maximum heart rate at the peak exercise load from the firstexperiment to the second decreased by 16.4%, declining from 146 to 122.A conventional ST segment method also indicates the absence of STdepression, but did not provide any quantification of such animprovement since this ischemic range is sub-threshold for the method.Unlike such a conventional method, the method of the present inventiondid provide such quantification. Applying the current invention, thecurves in FIG. 7 developed from the second experiment show that the areaof a quasi-stationary, QT-RR interval hysteresis decreased significantlyfrom the first experiment, and such hysteresis loop indicated that somelevel of exercise-induced ischemia still remained. A change in the shapeof the observed composite dispersion-restitution curves also indicatesan improvement since it changed from a flatter curve, similar to theflatter curves (with a lower excitability and a higher threshold,v_(r)=0.3 to 0.35) in FIG. 2, to a healthier (less ischemic) moreconvex-shape curve, which is similar to the lower threshold curves(v_(r)=0.2 to 0.25) in FIG. 2. Thus, FIG. 7 demonstrates that, due toits high sensitivity and high resolution, the method of the presentinvention can be used in the assessment of delicate alterations inlevels of cardiac ischemia, indicating changes of cardiovascular healthwhen treated by a conventional cardiovascular intervention.

EXAMPLE 7 Calculation of a Quantitative Indicium of CardiovascularHealth

This example was carried out with the data obtained in Examples 2-6above. FIG. 8 illustrates a comparative cardiovascular health analysisbased on ischemia assessment by the method of the present invention. Inthis example an indicium of cardiovascular health (here designated thecardiac ischemia index and abbreviated “CII”) was designed, which wasdefined as a quasi-stationary QT-RR interval hysteresis loop area, S,normalized by dividing it by the product(T_(RR,max)−T_(RR,min))(T_(QT,max)−T_(QT,min)). For each particularsubject this factor corrects the area for individual differences in theactual ranges of QT and RR intervals occurring during the tests underthe quasi-stationary treadmill exercise protocol. We determined minimumand maximum CII in a sample of fourteen exercise tests and derived anormalized index <CII>=(CII−CII_(min))/(CII_(max)−CII_(min)) varyingfrom 0 to 1. Alterations of <CII> in different subjects show that themethod of the present invention allows one to resolve and quantitativelycharacterize different levels of cardiac and cardiovascular health in aregion in which the conventional ST depression method is sub-thresholdand is unable to detect any exercise-induced ischemia. Thus, unlike arough conventional ST-segment depression ischemic evaluation, the methodof the present invention offers much more accurate assessing andmonitoring of small variations of cardiac ischemia and associatedchanges of cardiac or cardiovascular health.

EXAMPLE 8 Illustration of Rapid Sympatho-Adrenal Transients

FIG. 9 illustrates a typical rapid sympathetic/parasympathetic nervousand hormonal adjustment of the QT (panels A, C) and RR (panels B,D)intervals to an abrupt stop after 10 minutes of exercise with increasingexercise load. All panels depict temporal variations of QT/RR intervalsobtained from the right precordial lead V3 of the 12-lead multi-leadelectrocardiogram. A sampling rate with which a waveform analyzerdetermined QT and RR intervals was equal to 15 samples per minute. Ahuman subject (a 47 years-old male) was at rest the first 10 minutes andthen began to exercise with gradually (during 10 minutes) increasingexercise load (Panels A, B—to the left from the RR, QT minima). Then atthe peak of the exercise load (heart rate about 120 beat/min) thesubject stepped off the treadmill in order to initialize the fastest RRand QT interval's adaptation to a complete abrupt stop of the exerciseload. He rested long enough (13 minutes) in order to insure that QT andRR intervals reached post-exercise average stationary values. Panels Cand D demonstrate that the fastest rate of change of QT and RR intervalsoccurred immediately after the abrupt stop of the exercise load. Theserates are about 0.015 s/min for QT intervals while they vary from 0.28 sto 0.295 s and about 0.15 s/min for RR intervals while they grow from0.45 s to 0.6 s. Based on the above-described experiment, a definitionfor “rapid sympatho-adrenal and hormonal transients” or “rapid autonomicnervous system and hormonal transients” may be given.

Rapid transients due to autonomic nervous system and hormonal controlrefer to the transients with the rate of 0.15 s/min for RR intervals,which corresponds to the heart rate's rate of change of about 25beat/min, and 0.02 s/min for QT intervals or faster rates of change inRR/QT intervals in response to a significant abrupt change (stop orincrease) in exercise load (or other cardiac stimulus). The significantabrupt changes in exercise load are defined here as the load variationswhich cause rapid variations in RR/QT intervals, comparable in size withthe entire range from the exercise peak to the stationary average restvalues.

EXAMPLE 9 Illustration of a Quasi-Stationary Exercise Protocol

FIG. 10 illustrates a typical slow (quasi-stationary) QT (panel A) andRR (panel B) interval adjustment measured during gradually increasingand gradually decreasing exercise load in a right pre-cordial V3 lead ofthe 12 lead electrocardiogram recording. The sampling was 15 QT and RRintervals per minute. A male subject exercised during two consecutive 10minute long stages of gradually increasing and gradually decreasingexercise load. Both QT and RR intervals gradually approached the minimalvalues at about a peak exercise load (peak heart rate ˜120 beat/min) andthen gradually returned to levels that were slightly lower than theirinitial pre-exercise rest values. The evolution of QT and RR intervalswas well approximated by exponential fitting curves shown in gray inpanels A and B. The ranges for the QT-RR interval, there-and-back, timevariations were 0.34 s-0.27 s-0.33 s (an average rate of change ˜0.005s/min) and 0.79 s-0.47 s-0.67 s (an average rate of change ˜0.032 s/minor ˜6 beat/min) for QT and RR intervals, respectively. The standardroot-mean-square deviation, σ, of the observed QT and RR intervals,shown by black dots in both panels, from their exponential fits were onan order of magnitude smaller than the average difference between thecorresponding peak and rest values during the entire test. Thesedeviations were σ˜0.003 s for QT and σ˜0.03 s for RR intervals,respectively. According to FIG. 9 (panels C, D) such smallperturbations, when associated with abrupt heart rate changes due tophysiological fluctuations or due to discontinuity in an exercise load,may develop and decay faster than in 10 s, the time that is 60 timesshorter than the duration of one gradual (ascending or descending) stageof the exercise protocol. Such a significant difference between theamplitudes and time constants of the QT/RR interval gradual changes andabrupt heart rate fluctuations allows one to average these fluctuationsover time and fit the QT/RR protocol duration dynamics by an appropriatesmooth exponential-like function with a high order of accuracy. Asimultaneous fitting procedure (panels A, B) determines an algorithm ofa parametrical time dependence elimination from both measured QT/RR datasets and allows one to consider QT interval for each exercise stage as amonotonic function.

Based on the above-described experiment a definition for a gradual, or“quasi-stationary” exercise (or stimulation) protocol, can bequantitatively specified: A quasi-stationary exercise (or stimulation)protocol refers to two contiguous stages (each stage 3, 5, 8 or 10minutes or longer in duration) of gradually increasing and graduallydecreasing exercise loads or stimulation, such as:

1. Each stage's duration is approximately an order of magnitude (e.g.,at least about ten times) longer than the average duration (˜1 minute)of a heart rate adjustment during an abrupt stop of the exercise betweenaverage peak load rate (˜120-150 beat/min) and average rest (˜50-70beat/min) heart rate values.

2. The standard root-mean-square deviations of the original QT/RRinterval data set from their smooth and monotonic (for each stage) fitsare of an order of magnitude (e.g., at least about ten times) smallerthan the average differences between peak and rest QT/RR interval valuesmeasured during the entire exercise under the quasi-stationary protocol.

As shown above (FIG. 10) a gradual quasi-stationary protocol itselfallows one to substantially eliminate abrupt time dependent fluctuationsfrom measured QT/RR interval data sets because these fluctuations haveshort durations and small amplitudes. Their effect can be even furtherreduced by fitting each RR/QT interval data set corresponding to eachstage with a monotonic function of time. As a result the fitted QTinterval values during each exercise stage can be presented as asubstantially monotonic and smooth function of the quasi-stationaryvarying RR interval value. Presented on the (RR-interval,QT-interval)-plane this function gives rise to a loop, whose shape, areaand other measures depend only weakly on the details of thequasi-stationary protocol, and is quite similar to the hysteresis looppresented in FIG. 2. Similar to a generic hysteresis loop, this loop canbe considered as primarily representing electrical conduction propertiesof cardiac muscle.

It is well known that exercise-induced ischemia alters conditions forcardiac electrical conduction. If a particular individual has anexercise-induced ischemic event, then one can expect that the twoexperimental composite dispersion-restitution curves corresponding tothe ascending and descending stages of the quasi-stationary protocolwill be different and will form a specific quasi-stationary hysteresisloop. Since according to a quasi-stationary protocol the evolution ofthe average values of QT and RR intervals occurs quite slowly ascompared with the rate of the transients due tosympathetic/parasympathetic and hormonal control, the hysteresis looppractically does not depend on the peculiarities of the transients. Inthat case such a hysteresis can provide an excellent measure of gradualischemic exercise dependent changes in cardiac electrical conduction andcan reflect cardiac health itself and cardiovascular system health ingeneral.

It should be particularly emphasized that neither J. Sarma et al, supra,nor A. Krahn's et al. supra, report work based on collectingquasi-stationary dependences, which are similar to the QT-interval-RRinterval dependence, since in fact both studies were designed fordifferent purposes. To the contrary, they were intentionally based onnon-quasi-stationary exercise protocols that contained an abruptexercise stop at or near the peak of the exercise load. These protocolsgenerated a different type of QT/RR interval hysteresis loop with asubstantial presence of non-stationary sympatho-adrenal transients (seeFIG. 9 above). Thus these prior art examples did not and could notinclude data which would characterize gradual changes in the dispersionand restitution properties of cardiac electrical conduction, andtherefore included no substantial indication that could be attributed toexercise-induced ischemia.

EXAMPLES 10-12 Data Processing at Steps 44-45 a,b (FIGS. 4A and 4B)

The following Examples describe various specific embodiments forcarrying out the processing, shown in FIG. 4B, where the softwareimplemented at steps 44 b and 45 b performs the following major steps:

(i) Generates sufficiently smooth time dependent QT and RR data sets byaveraging/filtering and fitting these averaged data by exponential orany other suitable functions;

(ii) Combines into pairs the points of RR and QT data sets thatcorrespond to the same time instants, thereby generating smooth QT/RRcurves for the ascending and descending heart rate stages (branches) onthe (T_(RR),T_(QT))-plane or a similar plane or its image in computermemory;

(iii) Closes the ends of the QT/RR curves to transform them into aclosed loop and determines an area, S, or a similar measure of thedomain confined by the said loop and computes an index to provide aquantitative characteristic of cardiovascular health in a human subjectbased on a measure of this domain.

Each of these three major steps may consist of several sub steps, asillustrated in each of the methods shown in FIG. 11, FIG. 13 and FIG.15, FIG. 16 and as discussed in greater detail below.

EXAMPLE 10 A Method of Optimized Consolidation of a Moving Average,Exponential and Polynomial Fitting

1. Raw Data Averaging/Filtering (Box 1 in FIG. 11). The raw data setconsists of two subsets {t_(RR) ^(i),T_(RR) ^(i)} i=1, 2, . . .N_(RR)−1, and {t_(QT) ^(i),T_(QT) ^(i)}, i=1, 2, . . . N_(QT)−1, wheret_(x) ^(i) and T_(x) ^(i) denote the i-th sampling time instant and therespective, RR or QT, interval duration (subscript x stands for RR orQT). In order to simplify the notation we shall omit the subscripts RRand QT when it is applicable to both sub-samples. It is convenient torepresent each data point as a two-component vector u_(i)=(t^(i),T^(i)).The filtering procedure in this example comprises a moving averaging ofneighboring data points. We shall denote a moving overage over a set ofadjacent points by angular brackets with a subscript indicating thenumber of points included in the averaging operator. Thus, thepreliminary data filtering at this sub step is described by the equation$\begin{matrix}{{{\langle u_{i}\rangle}_{2} = {{\frac{1}{2}{\sum\limits_{j = i}^{j = {i + 1}}u_{j}}} = \frac{u_{i} + u_{i + 1}}{2}}},} & (10.1)\end{matrix}$

for each i=1, 2, . . . N−1, where N is a number of data points in thecorresponding (RR or QT) raw data set. Thus, the RR and QT intervaldurations and the corresponding sampling time points are identicallyaveraged in order to preserve the one-to-one correspondence betweenthem. This procedure removes the high frequency noise present in the rawdata. This preliminary smoothing can also be described in the frequencydomain and alternatively achieved via appropriate low-pass filtering.All the following processing pertinent to this example will be done onthe averaged data points <u_(i)>₂ and the angular brackets will beomitted to simplify the notation.

2. Preliminary Estimation of the t-Coordinates of the Minima (Box 2 inFIG. 11). The sub step consists of preliminary estimation of the timeinstants, t_(RR) ^(i) ^(_(m)) and t_(QT) ^(j) ^(_(m)) of the minima ofthe initially averaged RR-interval and QT-interval-data sets,respectively. The algorithm does a sequential sorting of the data setschoosing M data points corresponding to M least values of the RR- orQT-intervals and then averages the result. (In our examples, M=10.)First, the algorithm finds the u-vector u_(i) ₁ =(t^(i) ^(₁) ,T^(i) ^(₁)) corresponding to the shortest interval T^(i) ^(₁) . Next, this datapoint is removed from the data set {u_(i)} and the algorithm sorts theremaining data set and again finds a u-vector u_(i) ₂ =(t^(i) ^(₂) ,T^(i) ^(₂) ) corresponding to the shortest interval T^(i) ^(₂) . Theminimum point is again removed from the data sets and sorting isrepeated over and over again, until the M^(th) u-vector u_(i) _(m)=(t^(i) ^(_(m)) ,T^(i) ^(_(m)) ) corresponding to the shortest intervalT^(i) ^(_(m)) is found. Next, the algorithm averages all M pairs andcalculates the average minimum time coordinate {overscore (t)} definedas $\begin{matrix}{\overset{\_}{t} = {\frac{1}{M}{\sum\limits_{k = 1}^{M}t^{i_{k}}}}} & (10.2)\end{matrix}$

Finally, the algorithm determines the sampling time instant t^(i)^(_(m)) , which is nearest to {overscore (t)}. We thus arrive to t_(RR)^(i) ^(_(m)) and t_(QT) ^(j) ^(_(m)) for RR and QT data sets,respectively.

3. The First Correction of the Coordinates of the Preliminary Minima(Box 3 in FIG. 11). At this sub step the first correction to the minimumcoordinates t_(RR) ^(i) ^(_(m)) and t_(QT) ^(j) ^(_(m)) is found. Thispart of the algorithm is based on the iterative exponential fitting ofthe T-component of the initially filtered data set {u_(i)}={t^(i),T^(i)}by functions of the form

T(t)=Aexp[β|t−t ^(m)|],  (10.3)

where t^(m) is the time instant of the corresponding minimum determinedat the previous sub step (i.e., t^(m)=t_(RR) ^(i) ^(_(m)) forRR-intervals and t^(m)=t_(QT) ^(j) ^(_(m)) for QT-intervals). Thefitting is done separately for the descending (t<t^(m)) and ascending(t>t^(m)) branches of u(t) with the same value of constants A and t^(m)and different values of β for both branches. The initial value of A istaken from the preliminary estimation at sub step 2: A=T^(i) ^(_(m)) andt^(m)=t^(i) ^(_(m)) (i.e., A=T_(RR) ^(i) ^(_(m)) , t^(m)=t_(RR) ^(i)^(_(m)) for RR-intervals and A=T_(QT) ^(j) ^(_(m)) ,t^(m)=t_(QT) ^(j)^(_(m)) for QT-intervals). The initial value of constant β for eachbranch and each data sub set is obtained from the requirement that theinitial mean root square deviation σ=σ₀ of the entire correspondingbranch from its fit by equation (10.3) is minimum. In each subsequentiteration cycle new values of constants A and β are determined for eachbranch. At the beginning of each iteration cycle a constant A is takenfrom the previous step and the value of β is numerically adjusted tominimize the deviation value, σ. Such iterations are repeated while themean square deviation a is becoming smaller and are stopped when σreaches a minimum value, σ=σ_(min). At the end of this sub step thealgorithm outputs the corrected values A and β and the respective valuesof σ_(min) ^(RR) and σ_(min) ^(QT).

4. The Preliminary Smooth Curves (Box 4 in FIG. 11). The sub stepconsists of calculating a series of moving averages over p consecutivepoints for each data subset {u} as follows $\begin{matrix}{{u_{i}^{p} \equiv {\langle u_{i}\rangle}_{p}} = {\frac{1}{p}{\sum\limits_{j = 1}^{i + p - 1}{u_{j}.}}}} & (10.4)\end{matrix}$

We shall refer to the quantity p as the width of the averaging window.The calculation is performed for different values of p, and then theoptimum value of the width of the averaging window p=m is determined byminimizing the mean square deviation of the set {u_(i) ^(p)}={t_(i)^(p),T_(i) ^(p)} from its fit by Eq. (10.3) with the values ofparameters A, t^(m), and β determined at sub step 3. Having performedthis procedure for each component of the data set (RR and QT) we arriveto the preliminary smoothed data set {u_(i) ^(m)}={t_(i) ^(m),T_(i)^(m)}, where $\begin{matrix}{{T_{i}^{m} = {\frac{1}{m}{\sum\limits_{j = i}^{i + m - 1}T^{i}}}},\quad {t_{i}^{m} = {\frac{1}{m}{\sum\limits_{j = i}^{i + m - 1}t^{i}}}}} & (10.5)\end{matrix}$

The number of points in such a data set is N_(m)=N−m+1, where N is thenumber of data points after the initial filtering at sub step 1.

5. Correction of the Preliminary Smooth Curves and the Second Correctionof the QT and RR Minimal Values and its Coordinates (Box 5 in FIG. 11).At this sub step we redefine the moving averages (using a smalleraveraging window) in the vicinity of the minimum of quantity T (RR or QTinterval). This is useful to avoid distortions of the sought (fitting)curve T=T(t) near its minimum. The algorithm first specifies all datapoints {t^(i),T^(i)} such that T^(i) lie between${\min\limits_{i}{\left\{ T^{i} \right\} \quad {and}\quad {\min\limits_{i}\left\{ T^{i} \right\}}}} + {\sigma_{\min}.}$

These data points have the superscript values i from the following set$\begin{matrix}{I = {\left\{ {i:{T^{i} \in \left\lbrack {{\min\limits_{i}\left\{ T^{i} \right\}},{{\min\limits_{i}\left\{ T^{i} \right\}} + \sigma_{\min}}} \right\rbrack}} \right\}.}} & (10.6)\end{matrix}$

Let us denote by i₀εI and i_(q)εI the subscript values corresponding tothe earliest and latest time instants among {t_(i)} (iεI). We thus seti₀=min{I} and i_(q)=max{I}. Denoting the number of points in such a setby q_(RR) for the RR data and by q_(QT), for the QT data we determinethe width, q, of the averaging window as the minimum of the two,q=min{q_(QT),q_(RR)}. Now we write the moving average for the datapoints in the vicinity of the minimum as $\begin{matrix}{{u_{i}^{q} \equiv {\langle u_{i}\rangle}_{q}} = {\frac{1}{q}{\sum\limits_{j = i}^{i + q - 1}u_{j}}}} & (10.7)\end{matrix}$

Such modified averaging is applied to all consecutive data points u_(i)with the subscript i ranging from i₀ to i_(q). The final (smoothed) dataset consists of the first i₀−1 data points defined by Eq. (10.4) withi=1, 2, . . . i₀−1, q points defined by Eq. (10.7) with i=i₀, i₀+1, . .. , i_(q), and N−i_(q)−m points defined again by Eq. (10.4) withi=i_(q)+1, i_(q)+2, . . . , N−m+1. This the final set {{overscore(u_(i))}} can be presented as

{{overscore (u_(i))}}={ u _(i) ^(p) : iε{1, 2, . . . , i ₀−1}∪{i _(q)+1,. . . , N−m+1}}∪{u _(i) ^(q) : iε{i ₀ , i ₀+1, . . . , i _(q)}}  (10.8)

At the end of sub step 10.5 the algorithm determines the final minimumvalues of QT and RR interval and the corresponding time instants. Thealgorithm sorts the smoothed data sets (10.8) and determines {overscore(u)}_(min)≡({overscore (t)}_(min),{overscore (T)}_(min)) correspondingto the minimum value of {overscore (T)}_(i). This can be written as$\begin{matrix}{{{\overset{\_}{u}}_{\min} \equiv \left\{ {{\left( {{\overset{\_}{t}}_{i_{m}},{\overset{\_}{T}}_{i_{m}}} \right):{\overset{\_}{T}}_{i_{m}}} = {\min\limits_{k}\left\{ {\overset{\_}{T}}_{k} \right\}}} \right\}} = {{\overset{\_}{u}}_{i_{m}}.}} & (10.9)\end{matrix}$

6. Final Fitting and the Final Smooth QT and RR Curves (Box 6 in FIG.11).

At this sub step the parameters of functions representing final smoothQT and RR curves are found. First, each data set {{overscore (u)}_(i)}is split into two subsets {u⁻ ^(i)} and {u₊ ^(i)} corresponding to thedescending ({overscore (t)}_(i)≦{overscore (t)}_(i) _(m) ) and ascending({overscore (t)}_(i)≧{overscore (t)}_(i) _(m) ) branch, respectively. Wealso shift the time origin to the minimum point ({overscore (t)}_(i)_(m) ) and change the axis direction of the descending branch. Theseredefined variables are thus given by:

{u ⁻ ^(i)}={(t ⁻ ^(i) ,T ⁻ ^(i))≡({overscore (t)} _(i) _(m) −{overscore(t)} _(i) ,{overscore (T)} _(i)):i≦i _(m)}},  (10.10a)

{u ₊ ^(i)}={(t ₊ ^(i) ,T ₊ ^(i))≡({overscore (t)} _(i) −{overscore (t)}_(i) _(m) ,{overscore (T)} _(i)):i≧i _(m)}.  (10.10b)

Notice that the minimum point is included in both branches. Next weperform a linear regression by fitting each branch with a 4-th orderpolynomial function in the following form

 T _(±)(t _(±))=a _(±) t _(±) ⁴ +b _(±) t _(±) ³ +c _(±) y _(±) ²d  (10.11)

The linear term is not included into this expression since this functionmust have a minimum at t_(±)=0. The value of d is defined by

d={overscore (T)} _(min)  (10.12)

For computational convenience the variables us are transformed intoz±=T_(±)−d and then the coefficients a_(±), b_(±), and c_(±) aredetermined from the condition that expression for the error$\begin{matrix}{ɛ = {\sum\limits_{i}\left\lbrack {z_{\pm}^{i} - {a_{\pm}\left( t_{\pm}^{i} \right)}^{4} - {b_{\pm}\left( t_{\pm}^{i} \right)}^{3} - {c_{\pm}\left( y_{\pm}^{i} \right)}^{2}} \right\rbrack^{2}}} & (10.13)\end{matrix}$

where summation is performed over all points of the correspondingbranch, is minimized. We thus obtain four similar sets of linearalgebraic equations—two for each of the u_(±) branches of the two RR andQT data sets. These equations have the form $\begin{matrix}{{{\begin{matrix}{\sum\left( t_{\pm}^{i} \right)^{8}} & {\sum\left( t_{\pm}^{i} \right)^{7}} & {\sum\left( t_{\pm}^{i} \right)^{6}} \\{\sum\left( t_{\pm}^{i} \right)^{7}} & {\sum\left( t_{\pm}^{i} \right)^{6}} & {\sum\left( t_{\pm}^{i} \right)^{5}} \\{\sum\left( t_{\pm}^{i} \right)^{6}} & {\sum\left( t_{\pm}^{i} \right)^{5}} & {\sum\left( t_{\pm}^{i} \right)^{4}}\end{matrix}}\quad {\begin{matrix}a_{\pm} \\b_{\pm} \\c_{\pm}\end{matrix}}} = {\begin{matrix}{\sum{\left( t_{\pm}^{i} \right)^{4}z_{\pm}^{i}}} \\{\sum{\left( t_{\pm}^{i} \right)^{3}z_{\pm}^{i}}} \\{\sum{\left( t_{\pm}^{i} \right)^{2}z_{\pm}^{i}}}\end{matrix}}} & (10.14)\end{matrix}$

All summations are performed over all points of the branch. Now the QTand RR interval time dependences curves can be presented as the follows$\begin{matrix}{{T_{R\quad R}(t)} = \left\{ {\begin{matrix}{{T_{R\quad R}^{-}\left( {t - t_{\min}^{R\quad R}} \right)},} & {t \leq t_{\min}^{R\quad R}} \\{{T_{R\quad R}^{+}\left( {t - t_{\min}^{R\quad R}} \right)},} & {t \geq t_{\min}^{R\quad R}}\end{matrix}{and}} \right.} & (10.15) \\{{T_{Q\quad T}(t)} = \left\{ \begin{matrix}{{T_{Q\quad T}^{-}\left( {t - t_{\min}^{Q\quad T}} \right)},} & {t \leq t_{\min}^{Q\quad T}} \\{{T_{Q\quad T}^{+}\left( {t - t_{\min}^{Q\quad T}} \right)},} & {t \geq t_{\min}^{Q\quad T}}\end{matrix} \right.} & (10.16)\end{matrix}$

where T_(RR) ^(±)(t) and T_(QT) ^(±)(t) are the fourth order polynomialsgiven by Eq. (10.11) and t_(min) ^(RR) and t_(min) ^(QT) are the timecoordinates of the corresponding minima defined by Eq. (10.9). Thus,formulas (10.10)-(10.16) determine the final smooth QT and RR curveswith minima defined by formula (10.9).

7. Final Smooth Hysteresis Loop (Box 7 in FIG. 11). At this sub-step thesoftware first generates a dense (N+1)-point time-gridτ_(k)=t_(start)+k(t_(end)−t_(start))/N, where k=0, 1, 2, . . . ,N(N=1000 in this example) and t_(start) and t_(end) are the actual valuesof time at the beginning and end of the measurements, respectively. Thenit computes the values of the four functions T_(RR) ^(±)(τ−t_(min)^(RR)) and T_(QT) ^(±)(τ−t_(min) ^(QT)) on the grid, whichparametrically represents the final smooth curves (T_(RR) ^(±)(τ−t_(min)^(RR)), T_(QT) ^(±)(τ−t_(min) ^(QT))) in computer memory for theascending (+) and descending (−) branches, respectively. This procedureis a computational equivalent of the analytical elimination of time.Next, the software also plots these smooth curves on the(T_(RR),T_(QT))-plane or on another, similar plane, such as(f_(RR),T_(QT)), where f=1/T_(RR) is the instantaneous heart rate.Finally, the algorithm adds to the curves a set of points representing aclosing line, which connects the end point of the lower (descending)branch with the initial point on the of the upper (ascending) branchand, thus, generates a closed QT/RR hysteresis loop.

8. A Measure of the Domain Bounded by the QT/RR Hysteresis Loop (Box 8in FIG. 11). At this sub step a measure of the domain inside the QT/RRhysteresis loop is computed by numerically evaluating the followingintegral (see definition above): $\begin{matrix}{S = {\int_{\Omega}{\int{{\rho \left( {T_{RR},T_{QT}} \right)}{T_{RR}}{T_{QT}}}}}} & (10.17)\end{matrix}$

where Ω is the domain on the (T_(RR),T_(QT))-plane with the boundaryformed by the closed hysteresis loop, and ρ(T_(RR),T_(QT)) is anonnegative (weight) function. In this example we can takeρ(T_(RR),T_(QT))=1 so that S coincides with the area of domain Ω, or weset ρ=1/(T_(RR))² so S coincides with the dimensionless area of thedomain inside the hysteresis loop on the (f,T_(QT))-plane, wheref=1/T_(RR) is the heart rate.

EXAMPLE 11 A Method of a Sequential Moving Average

1. Raw Data Averaging/Filtering. The sub step (similar to 10.1) consistsof raw data averaging (filtering) according to formula (10.4). This isperformed for a preliminary set of values of the averaging window width,p.

2. Final Moving Average Smoothing. The sub step includes subsequentfinal smoothing of the preliminary smoothed data represented by the set{u_(i) ^(p)} found at the previous step: as follows. $\begin{matrix}{{\overset{\_}{u^{p}} \equiv {\langle u_{i}^{p}\rangle}_{m_{f}}} = {\frac{1}{m_{f}}{\sum\limits_{j = i}^{j = {i + m_{f} - 1}}{u_{j}^{p}.}}}} & (11.1)\end{matrix}$

The window width m_(f) is varied numerically to achieve optimumsmoothness and accuracy of the fit. The optimally averaged data pointsform smooth curves on the corresponding planes (FIGS. 12,14).

3. A Measure of the Domain Inside the QT/RR Hysteresis Loop. Theprocedure on this sub step is as defined in Example 10, step 8, above.

EXAMPLE 12 A Method of Optimized Nonlinear Transformations

FIG. 15 illustrates major steps in the data processing procedureinvolving our nonlinear transformations method. The first three stagesfor the RR and QT data sets are quite similar and each results in thecomputation of the fitted bird-like curves, T^(RR)=T^(RR)(t) andT^(QT)=T^(QT)(t), on a dense time-grid. Having computed both bird-likecurves one actually completes the data processing procedure, becauseafter appropriate synchronization, these two dependences parametricallyalong with a closing line represent the sought hysteresis loop on the(T^(RR), T^(QT)), or similar, plane. We will describe our method ingeneral terms equally applicable for the QT and RR interval data sets,and indicate the specific instants where there is a difference in thealgorithm.

1. Preliminary Data Processing Stage. Let {T_(k)}, k=1, 2, . . . , N, bea set of the measured RR or QT interval durations, and {t_(k)} be a setof the corresponding time instants, so that t₁ and t_(N) are thestarting and ending time instants (segments) of the entire record. Thefirst three similar stages (stages 1 through 3 in FIG. 15) are thepreliminary stage, the secondary, nonlinear-transformation stage, andthe computational stage. A more detailed data flow chart for thesestages is shown in FIG. 16. The preliminary stage, indicated by boxes 1through 7 in FIG. 16, is a combination of traditional data processingmethods and includes: smoothing (averaging) the data sets (1),determination of a region near the minimum (2), and fitting a quadraticparabola to the data in this region (3), checking consistency of theresult (4), renormalizing and centering the data at the minimum (5),cutting off the data segments outside the exercise region and separatingthe ascending and descending branches (6), and finally filtering off adata segment in near the minimum (7). Let us discuss these steps in moredetail.

Box 1 in FIG. 16, indicates the moving averaging and itself consists oftwo steps. First, we specify the initial value of the moving averageprocedure parameter m, as $\begin{matrix}{m = {\max \left\{ {{r\left( \frac{N}{N_{c}} \right)},m_{\min}} \right\}}} & (12.1)\end{matrix}$

where r(x) is the integer closest to x, and the values of N_(c) andm_(min) are chosen depending on the number N of data points and theamount of random fluctuations in the data (the size of the randomcomponent in the data). In our examples we have chosen N_(c)=100 andm_(min)=3. The value of m can be redefined iteratively at the laterstages and its choice will be discussed therein. Next we compute themoving average for {t_(i)} and {T_(i)} data sets with the givenaveraging parameter m as follows: $\begin{matrix}{{{\langle t_{k}\rangle}_{m} = {\frac{1}{m}{\sum\limits_{i = 1}^{m}t_{k + i}}}},{{\langle T_{k}\rangle}_{m} = {\frac{1}{m}{\sum\limits_{i = 1}^{m}T_{k + i}}}}} & (12.2)\end{matrix}$

The subscript m will be omitted below if m is fixed and no ambiguity canarise. The next step in our algorithm is the initial determination of atime interval on which the parabolic fit will be performed, (theparabolic fit interval). This step is represented in FIG. 16 by Box 2.We note that this data subset can be redefined at a later stage if acertain condition is not satisfied. In the current realization of ouralgorithm this region defined differently for {t_(i),T_(i) ^(RR)} and{t_(i),T_(i) ^(QT)} data sets. For the data set {t_(i),T_(i) ^(RR)} theinitial parabolic fit segment is defined as the data segment{t_(i),T_(i) ^(RR)} with all sequential values of i between i₁ and i₂where i₁=n_(min)−Δm and i₂=n_(min)+Δm, and the integer parametersn_(min) and Δm are defined as follows. The number n_(min) determines thetime instant t_(n) _(min) among the original set of time instants whichis the closest to the minimum on the averaged data set{<t_(i)>,<T_(i)>}. In other words, t_(n) _(min) is the nearest to theaverage time instant <t_(M)> which corresponds to the minimum value ofthe average RR-interval <T_(i) ^(RR)>, that is, the time instant withthe subscript value M defined by the condition $\begin{matrix}{{\langle T_{M}^{RR}\rangle} = {\min\limits_{i}\left\{ {\langle T_{i}^{RR}\rangle} \right\}}} & (12.3)\end{matrix}$

The value of Δm is linked to the value of m by the condition Δm=2m. Thelink between Δn and m arises from the requirement that the algorithm isstable and consistent. The consistency is the requirement that thepositions of the minimum of the curve obtained by moving averaging andby quadratic fitting were approximately the same. On the other hand, itis also important that the value of m is sufficiently small becausequadratic fitting is done with the purpose to describe the data onlylocally in the immediate vicinity of the minimum.

For the data set {t_(i),T_(i) ^(QT)} the initial parabolic fit segmentis defined as the data subset that consists of all consecutive pointsbelonging to the lower portion of the non-averaged {T_(i) ^(QT)} dataset. We thus define i₁ as the first (minimum) number i such that$\begin{matrix}{T_{i}^{Q\quad T} \leq {{\min\limits_{j}\left( T_{j}^{Q\quad T} \right)} + {R\left\lbrack {{\max\limits_{j}\left( T_{j}^{Q\quad T} \right)} - {\min\limits_{j}\left( T_{j}^{Q\quad T} \right)}} \right\rbrack}}} & (12.4)\end{matrix}$

where R is a parameter, 0<R<1, that determines the portion of the datato be fitted with the quadratic parabola. In our calculations we setR=⅛=0.125, so we fit with the parabola the data points that correspondto the bottom 12.5% of the interval durations. Thus, the subscript i, isthe first (smallest) value of i such that condition (12.4) is satisfied.Similarly, i₂ is the last (greatest) value of i such that condition(12.4) is satisfied. The initial fit region is then defined as thefollowing non-averaged data subset: {(t_(i),T_(i) ^(QT)): i=i₁,i₁+1,i₁+2, . . . , i₂}. This method can also be used for determining aninitial data segment for the quadratic polynomial fitting of the RR-dataset.

At the next step, shown by box 3 in FIG. 12.2, we fit the data in thisregion (for each data set) by a parabola so that the data areapproximately represented by the equation

T _(k) ≈P ₁ t _(k) ² +P ₂ t _(k) +P ₃ , k=j ₁ , j ₁+1,j ₁+2, . . . , j₂.  (12.5)

This is done using usual linear regression on this data subset. At thenext step (Box 4 in FIG. 16) we check if the parabola has a minimum(i.e., if P₁>0). If this condition is satisfied, the determination ofthe parabolic fit interval and the fitting parabola itself is completed.Otherwise, we enter the loop indicated by boxes 1 a through 3 a in FIG.16. The first step there is similar to the above second step utilizedfor the RR interval data set and defines an extended segment for theparabolic fitting. This is done by replacing m with m+1 and using thisnew value of m to redefine Δm=2m and also calculate new averaged datasets in accordance with Eq. (12.2) as indicated by Box 1 a in FIG. 16.This allows us to evaluate a new value of n_(min) and new values ofi₁=n_(min)−Δm and i₂=n_(min)+Δm with new value of m (Box 2 a). Then theparabolic fit is done again (Box 3 a) and the condition P₁>0, that theparabola has a minimum, is checked again. If it is satisfied, thedetermination of the fit interval and the quadratic fit coefficientsprocedure is completed. Otherwise we replace m with m+1 and repeat theprocess again and again until the condition P₁>0 is satisfied. Thiscondition ensures that the extremum of the quadratic parabola is aminimum indeed. By the very design of the exercise protocol the averageheart rate reaches a certain maximum somewhere inside the load stage andtherefore corresponding average RR-interval reaches a minimum. Thisensures that a so-defined data segment exists and is unique, andtherefore the coefficients of the quadratic parabola are well defined.In short, we use the shortest data segment that is centered around theminimum of the averaged data set and that generates a quadratic parabolawith a minimum (P₁>0).

The parabolic fit defines two important parameters of the dataprocessing procedure, the position (t_(min),T_(min)) of the minimum onthe (t, T)-plane as follows $\begin{matrix}{{t_{\min} = {- \frac{P_{2}}{2P_{1}}}},{T_{\min} = {P_{3} - {\frac{P_{2}^{2}}{4P_{1}}.}}}} & (12.6)\end{matrix}$

These parameters are final in the sense that our final fit curve willalways pass through and have a minimum at the point (t_(min),T_(min)).The coordinates (t_(min),T_(min)) thus constitute parameters of ourfinal fit bird-like curve. Having found the ordinate T_(min) of theminimum we can renormalization of the T-data set as follows:$\begin{matrix}{y_{k} = {\frac{T_{k}}{T_{\min}}.}} & (12.7)\end{matrix}$

We also take the abscissa of the parabola's minimum t_(min) as the timeorigin and define the time components of the data points as follows

t _(i) ⁻ =t _(i) −t _(min) , t _(i)≦0,

t _(j) ⁺ =t _(j) −t _(min) t _(j)>0.  (12.8)

These two data transformations are indicated by Box 5 in FIG. 16. Wealso restrict the data set only to the exercise period, plus some shortpreceding and following intervals (Box 5). The conditions t_(i) ⁻≦0, andt_(j) ⁺>o define the descending, {t_(i) ⁻,T_(i)}, and ascending, {t_(j)⁺, T_(j)}, branches, respectively, so the corresponding data points canbe readily identified and separated (Box 6). Given the durations t_(d)and t_(a) of the descending and ascending load stage, respectively, wecan reduce the original set by cutting off the points on the descendingbranch with t_(i) ⁻<−t_(d) and the points on the ascending branch witht_(j) ⁺>t_(a) (Box 6 in FIG. 16). This determines the minimum value i₀of subscript i for the descending branch, and the maximum value j_(max)of subscript j on the ascending branch.

The final step of the preliminary data processing is the conditionalsorting (Box 7). The conditional sorting removes all consecutive pointssuch that at least one of them falls below the minimum of the parabola.The removal of the points below the minimum is necessary because thenonlinear transformation is possible only when y_(i)≧1. Eliminating onlyseparate points below the minimum y=1 would create a bias in the data.Therefore, we have to eliminate an entire segment of the data in thevicinity of the minimum. It should be remembered though, that thesepoints have already been taken into account in the above quadraticfiltering procedure that determines (t_(min),T_(min)) via Eq. (12.6).

Thus, the preliminary data processing results in two data setscorresponding to the descending and ascending load stages. Thedescending data set is defined as a set of consecutive pairs (t_(i) ⁻,y_(i))≡(t_(i) ⁻, y_(i) ⁻) with i=i₀, i₀+1, i₀+2, . . . , i_(max), wherei_(max) is determined by the conditional sorting as the largestsubscript i value still satisfying the condition y_(i)≧1. Similarly, theascending data set is defined as a set of consecutive pairs (t_(i)⁺,y_(i))≡(t_(I) ⁺,y_(i) ⁺) with j=j_(min), j₀+1, j₀+2, . . . , j_(max),where j_(min) is determined by the conditional sorting as the firstsubscript j value on the ascending branch starting from which thecondition y_(j)≧1 is satisfied for all subsequent j.

2. Secondary Data Processing. At the second stage we introduce afundamentally new method of nonlinear regression by means of twoconsecutive optimal nonlinear transformations. The idea of the method isto introduce for each branch two appropriate nonlinear transformationsof the dependent and independent variables, y=f(u) and u=φ(t), bothtransformations depending on some parameters, and choose the values ofthe parameters in such a way that the composition of thesetransformations f(φ(t_(i))) would provide an approximation for y_(i).Let (t_(i) ⁻, y_(I) ⁻) and (t_(i) ⁺, y_(i) ⁺) be the cut, conditionallysorted and normalized data set corresponding to the descending andascending branches representing the dynamics of the RR- or QT-intervalsduring exercise. The nonlinear transformation y=>u is defined via asmooth function

 y=f _(γ)(u),  (12.9)

that has a unit minimum at u=1, so that f_(γ)(1)=1, f_(γ)′(1)=0, andf_(γ)(u) grows monotonously when u≧1 and decreases monotonously whenu≦0. The subscript y represents a set of discrete or continuousparameters and indicates a particular choice of such a function. Let usdenote by f_(γ) ⁻(u) the monotonously decreasing branch of f_(γ)(u) andits monotonously increasing branch, by f_(γ) ⁺(u). We can thus write$\begin{matrix}{{f_{\gamma}(u)} = \left\{ \begin{matrix}{{f_{\gamma}^{-}(u)},{{{when}\quad u} \leq 1},} \\{{f_{\gamma}^{+}(u)},{{{when}\quad u} \geq 1.}}\end{matrix} \right.} & (12.10)\end{matrix}$

Let u=g_(γ) ⁺(y) and u=g_(γ) ⁻(y) be the inverse functions for therespective branches of f_(γ)(u). The functions g_(γ) ⁺(y) and f_(γ) ⁺(u)are monotonously increasing, while the functions g_(γ) ⁻(y) and f_(γ)⁻(u) are monotonously decreasing. Let {t_(i), y_(i) ⁻} represent thedata for the descending segment of the data set, i.e. t_(i)<t_(min) and{t_(i), y_(i) ⁺} represent the data for the ascending segment of thedata set i.e. for t_(i)>t_(min). The transformation

u _(γ,i) ⁻ =g _(γ) ⁻(y _(i) ⁻)  (12.11)

maps the monotonously decreasing (on the average) data set {t_(i), y_(i)⁻} into a monotonously increasing one:

{t _(i) ,y _(i) ⁻ }=>{t _(i) ,g _(γ) ⁻(y _(i) ⁻)}≡{t _(i) ,u _(γ,i)⁻}  (12.12)

Moreover, the average slope of the original data set is decreasing ast_(i) approaches t_(min) and eventually vanishing at the minimum. Incontrast, the average slope of the transformed data set is alwaysnonzero at t=t_(min). Similarly, the transformation

 u _(γ,j) ⁺ =g _(γ) ⁺(y _(j) ⁺)  (12.13)

maps the monotonously increasing (on the average) data set {t_(i), y_(i)⁺} into a monotonously increasing one:

{t _(j) ,y _(j) ⁺ }=>{t _(j) ,g _(γ) ⁺(y _(j) ⁺)}≡{t _(j) , u _(γ,j)⁺}.  (12.14)

In our examples we used a discrete parameter γ taking two values γ=1 andγ=2 that correspond to two particular choices of the nonlineary-transformation. The first case (γ=1) is described by the equations

y=f ₁(u)≡1+(u−1)² ; u ⁻ =g ₁ ⁻(y)≡y−{square root over (y²−1)}, u ⁺ =g ₁⁺(y)≡y+{square root over (y²−1)}.  (12.15)

The second case, γ=2, is described by the equations $\begin{matrix}{{{y = {{f_{2}(u)} \equiv {u + \frac{1}{u}}}};}{{u^{-} = {{g_{2}^{-}(y)} \equiv {1 - \sqrt{y - 1}}}},{u^{+} = {{g_{2}^{+}(y)} \equiv {1 + {\sqrt{y - 1}.}}}}}} & (12.16)\end{matrix}$

Both functions reach a minimum y=1 at u=1. An example of such a functiondepending on a continuous parameter γ>0 is given by $\begin{matrix}{{{f_{\gamma}(u)} = {A_{Y}\left\{ {\frac{1}{\gamma^{2} + {b_{\gamma}u}} + \frac{\gamma^{2}b_{\gamma}u}{{\gamma^{2}b_{\gamma}u} + 1}} \right\}}},{b_{\gamma} \equiv {1 + \gamma + {\frac{1}{\gamma}.}}}} & (12.17)\end{matrix}$

The parameter b_(γ) has been determined from the condition that fγ(u)has a minimum at u=1 and the coefficient A_(γ) is determined by thecondition f_(γ)(1)=1, which yields $\begin{matrix}{A_{\gamma} = \frac{\gamma^{3} + \gamma^{2} + \gamma + 1}{\gamma^{3} + \gamma^{2} + {2\gamma}}} & (12.18)\end{matrix}$

In our numerical examples below we utilize the discrete parameter casewith γ taking two values, 1 and 2. The original and transformed sets areshown in FIGS. 17 (RR intervals) and 18 (QT-intervals). Panels A in bothfigures show the original data sets on the (t,T)-plane and panels B andC show the transformed sets on the (t,u)-plane, for γ=1 and for γ=2,respectively. The parabola minima on panels A and C are marked with acircled asterisk. The original data points concentrate near anon-monotonous curve (the average curve). The data points on thetransformed plane concentrate around a monotonously growing (average)curve. Moreover, the figure illustrates that the transformation changesthe slope of the average curve in the vicinity of t=t_(min) from zero toa finite, nonzero value. On the (t−t_(min),u)-plane the pointcorresponding to the parabola's minimum is (0,1). This point is alsomarked by a circled asterisk on panels B and C of FIGS. 17 and 18.

Let us introduce a pair of new time variables τ⁻ and τ⁺ for thedescending and ascending branches, respectively. We shall count them offfrom the abscissa of the minimum of the fitted parabola and set

τ_(i) ⁻ =t _(min) −t _(i) , t _(i)≦t_(min) , i=1, 2, . . . ,I ⁻

τ_(j) ⁺ =t _(j) −t _(min), t_(j)≧t_(min), j=1, 2, . . . ,J⁺  (12.19)

where I⁻ and J⁺ are the number of data points on the descending andascending branches, respectively. The (formerly) descending branch canbe treated in exactly the same way as the ascending one ifsimultaneously with the time inversion given by the first line in Eq.(12.19) we perform an additional transformation of the descending branchordinates as follows

v _(k)=1−u _(k) ⁻.  (12.20)

In these variables both branches (τ_(i) ⁻, v_(i)) and (τ_(j) ⁺,u_(j) ⁺)are monotonously growing and start from the same point (τ=0,u=1) atwhich both have nonzero slope and possess similar behavior (convexity).

Since both branches are treated in exactly the same way, we shallsimplify the notation and temporarily omit the superscripts ± and write(τ_(k),u_(k)) for any of the pairs (τ_(i) ⁻,v_(i)) or (τ_(j) ⁺,u_(j) ⁺).We shall fit the data set {u_(k)} with {φ(α, β, τ_(k))}, that isrepresent {u_(k)} as

u _(k)≈φ(α,β,K,τ _(k))  (12.21)

where the function φ depends linearly on K and is defined as

φ(α,β, K, τ)≡1+Kξ(α,β,t)  (12.22)

where${\xi \left( {\alpha,\beta,\tau} \right)} = \left\{ \begin{matrix}{\frac{\alpha}{\beta}\left( {1 + \frac{\tau}{\alpha}} \right)^{\beta}} & {{{when}\quad \beta} > 0} \\{s \equiv {\alpha \quad {\ln \left( {1 + \frac{\tau}{\alpha}} \right)}}} & {{{when}\quad \beta} = 0} \\{\frac{\alpha}{1 + \beta}\left\lbrack {\left( {1 + \frac{s}{\alpha}} \right)^{1 + \beta} - 1} \right\rbrack} & {{{when}\quad - 1} \leq \beta < 0}\end{matrix} \right.$

A family of functions ξ(α,β,τ) is shown in FIG. 19 for fifteen values ofparameter β. The parameter α is completely scaled out by plotting thefunction on the plane (τ/α,ε/α). The function ξ(α,β,τ) is continuous inall three variables and as a function of τ at fixed α and β has a unitslope at τ=0, ξ′(α,β,0)=1. Therefore, at τ→0 the function ξ possesses avery simple behavior, ξ˜τ, which is independent of α and β (the size ofthe region of such behavior of course depends on α and β). The functionξ possesses the following important feature: when β passes through thepoint β=0, its asymptotic behavior at τ→∞ continuously changes from thepower function, ξ˜τ^(β) at β>0, through ξ˜ln(τ) at β=0, to a power ofthe logarithm, ξ˜ln^(1+β)(τ) when −1<β<0. When β→−1, the behavior of ξchanges once more, and becomes ξ˜ln(ln(τ)). The convexity of anyfunction of the family is the same when β<1.

We shall explicitly express parameter K via α and β using therequirement for a given pair of α and β Eq-s. (12.22) and (12.23) ensurethe best data fit in the u-space in a certain vicinity of the point(τ=0,u=1). Let K₁ be the number of points where the fit is required. Thecorresponding quadratic error is then a function of K, α and β that canbe written as $\begin{matrix}{{ɛ^{(u)}\left( {K,\alpha,\beta} \right)} = {\sum\limits_{k \leq K_{1}}\left\lbrack {u_{k} - {K\quad {\phi \left( {\alpha,\beta,T_{k}} \right)}}} \right\rbrack^{2}}} & (12.24)\end{matrix}$

and the requirement of its minimum immediately yields the followingexpression for K $\begin{matrix}{K = {{K\left( {\alpha,\beta} \right)} \equiv \frac{\sum\limits_{k \leq K_{1}}{u_{k}{\phi \left( {\alpha,\beta,\tau_{k}} \right)}}}{\sum\limits_{k \leq K_{1}}{\phi^{2}\left( {\alpha,\beta,\tau_{k}} \right)}}}} & (12.25)\end{matrix}$

In our calculations we used such K₁ value that would include alladjacent points with the values of u between u=1 and u=1+0.4(u_(max)−1). We have thus reduced the number of fitting parameters inour fitting procedure to two continuous parameters, α and β, and onediscrete parameter, γ. The fitting function thus becomes

y _(k) ≈f _(γ)(1+K(α,β)ξ(α,β,τ_(k)))  (12.26)

The values of parameters α, β, and K (and γ) are now directly determinedby the condition that the fit error in the y-space $\begin{matrix}{{ɛ_{\gamma}^{(y)}\left( {\alpha,\beta} \right)} = {\sum\limits_{k}\left\lbrack {y_{k} - {f_{\gamma}\left( {1 + {{K\left( {\alpha,\beta} \right)}{\phi \left( {\alpha,\beta,\tau_{\lambda}} \right)}}} \right)}} \right\rbrack^{2}}} & (12.27)\end{matrix}$

is minimum. The sum in Eq. (12.27) is evaluated numerically on a grid(α,β) values for γ equal 1 and 2. Then the values of α, β and γ thatdeliver a minimum to ε_(γ) ^((Y)) are found via numerical trials.Calculations can then be repeated on a finer grid in the vicinity of thefound minimum.

Having found parameters α_(min), β_(min) and γ_(min) for the ascendingbranch we generate a dense t-grid {t_(s), s=1, 2, . . . , N} andcalculate the corresponding values of the interval duration as

T _(S) =T _(min) f _(Y) _(min) (1+K(α_(min),β_(min))ξ(α_(min),β_(min) ,t_(s) −t _(min))).  (12.26)

A similar dense representation of the descending branch can becalculated in exactly the same way. The resulting bird-like curves areillustrated in panels A and C of FIG. 20. The actual absolute andrelative errors are indicated in the captions. The right hand sidepanels B and D represent hysteresis curves in two differentrepresentations and each resulting from the curves shown in Panels A andC. The following computations of the hysteresis loop and its measuregiven by Eq. (10.17) is then performed as described in Example 10.

EXAMPLE 13 Creation of an RR-Hysteresis Loop With the Procedures ofExamples 10-12

In addition to the procedures generating a hysteresis loop on the plane(QT-interval versus RR-interval) or an equivalent plane, one canintroduce and assess a separate hysteresis of the duration ofRR-interval versus exercise workload, which gradually varies,there-and-back, during the ascending and descending exercise stages. TheRR-hysteresis can be displayed as loops on different planes based onjust a single RR data set {t_(RR) ^(i), T_(RR) ^(i)} analysis. Forexample, such a loop can be displayed on the (τ^(i), T_(RR) ^(i))-plane,where τ^(i)=|t_(RR) ^(i)−t_(min)| and t_(min) is the time instantcorresponding to the peak of the exercise load, or the center of themaximum load period, which may be determined according to numericaltechniques described in the examples 10-12. The RR loop can also beintroduced on the (W(t_(RR) ^(i)), T_(RR) ^(i)) or (τ^(i), (T_(RR)^(i))⁻¹) planes. Here W(t_(RR) ^(i)) is a workload that varies versusexercise stages, i.e. time and (T_(RR) ^(i))⁻¹ represents the heartrate.

In order to apply a numerical technique from the Example 10 (or anyother as in Examples 11 or 12), one repeats essentially the samecomputational steps described in these examples. However, instead ofconsidering both QT-{t_(QT) ^(i),T_(QT) ^(i)} and RR-{t_(RR) ^(i),T_(RR)^(i)} interval data sets, only a single RR data set is numericallyprocessed throughout the whole sequence of the described stages for acreation of a hysteresis loop. In this case variables τ^(i), (T_(RR)^(i))⁻¹ or W(t_(RR) ^(i)) play the role of the second alternatingcomponent that along with the first T_(RR) ^(i) variable forms theRR-hysteresis plane.

The foregoing examples are illustrative of the present invention and arenot to be construed as limiting thereof The invention is defined by thefollowing claims, with equivalents of the claims to be included therein.

That which is claimed is:
 1. A method of assessing cardiac ischemia in asubject to provide a measure of cardiac or cardiovascular health in thatsubject, wherein said subject is afflicted with coronary artery disease,said method comprising the steps of: (a) collecting a first RR-intervaldata set from said subject during a stage of gradually increasing heartrate; (b) collecting a second RR-interval data set from said subjectduring a stage of gradually decreasing heart rate, with said first andsecond RR-interval data sets being collected while minimizing theinfluence of rapid transients due to autonomic nervous system andhormonal influence on said data sets; (c) comparing said firstRR-interval data set to said second RR-interval data set to determinethe difference between said data sets; and (d) generating from saidcomparison of step (c) a measure of cardiac ischemia in said subject,wherein a greater difference between said first and second data setsindicates greater cardiac ischemia and lesser cardiac or cardiovascularhealth in said subject.
 2. The method according to claim 1, wherein saidfirst and second RR-interval data sets are collected underquasi-stationary conditions.
 3. The method according to claim 1, whereinsaid stage of gradually increasing heart rate and said stage ofgradually decreasing heart rate are each at least 3 minutes in duration.4. The method according to claim 1, wherein said stage of graduallyincreasing heart rate and said stage of gradually decreasing heart rateare together carried out for a total time of from 6 minutes to 40minutes.
 5. The method according to claim 1, wherein: both said stage ofgradually increasing heart rate and said stage of gradually decreasingheart rate are carried out between a peak rate and a minimum rate; andsaid peak rates of both said stage of gradually increasing heart rateand said stage of gradually decreasing heart rate are the same.
 6. Themethod according to claim 5, wherein: said minimum rates of both saidstage of gradually increasing heart rate and said stage of graduallydecreasing heart rate are substantially the same.
 7. The methodaccording to claim 1, wherein said stage of gradually decreasing heartrate is carried out at at least three different heart-rate stimulationlevels.
 8. The method according to claim 7, wherein said stage ofgradually increasing heart rate is carried out at at least threedifferent heart-rate stimulation levels.
 9. The method according toclaim 1, wherein said stage of gradually increasing heart rate and saidstage of gradually decreasing heart rate are carried out sequentially intime.
 10. The method according to claim 1, wherein said comparing stepis carried out by generating curves from each of said data sets.
 11. Themethod according to claim 10, wherein said comparing step is carried outby comparing the shapes of said curves from data sets.
 12. The methodaccording to claim 10, wherein said comparing step is carried out bydetermining a measure of the domain between said curves.
 13. The methodaccording to claim 10, wherein said comparing step is carried out byboth comparing the shapes of said curves from data sets and determininga measure of the domain between said curves.
 14. The method according toclaim 10, further comprising the step of displaying said curves.
 15. Themethod according to claim 1, wherein said heart rate during said stageof gradually increasing heart rate does not exceed more than 120 beatsper minute.
 16. The method according to claim 1, wherein said heart rateduring said stage of gradually increasing heart rate exceeds 120 beatsper minute.
 17. The method according to claim 1, further comprising thestep of: (e) comparing said measure of cardiac ischemia duringstimulation to at least one reference value; and then (f) generatingfrom said comparison of step (e) a quantitative indicium of cardiac orcardiovascular health for said subject.
 18. The method according toclaim 17, further comprising the steps of: (g) treating said subjectwith a cardiovascular therapy; and then (h) repeating steps (a) through(f) to assess the efficacy of said cardiovascular therapy, in which adecrease in the difference between said data sets from before saidtherapy to after said therapy indicates an improvement in cardiac healthin said subject from said cardiovascular therapy.
 19. The methodaccording to claim 18, wherein said cardiovascular therapy is selectedfrom the group consisting of aerobic exercise, muscle strength building,change in diet, nutritional supplement, weight loss, stress reduction,smoking cessation, pharmaceutical treatment, surgical treatment, andcombinations thereof.
 20. The method according to claim 17, furthercomprising the step of assessing from said quantitative indicum thelikelihood that said subject is at risk to experience a futureischemia-related cardiac incident.
 21. A method of assessing cardiacischemia in a subject to provide a measure of cardiac or cardiovascularhealth in that subject, wherein said subject is afflicted with coronaryartery disease, said method comprising the steps of: (a) collecting afirst RR-interval data set from said subject during a stage of graduallyincreasing exercise load and gradually increasing heart rate; and then,after an abrupt stop in exercise, (b) collecting a second RR-intervaldata set from said subject during a stage of rest and graduallydecreasing heart rate; (c) comparing said first RR-interval data set tosaid second RR-interval data set to determine the difference betweensaid data sets; and (d) generating from said comparison of step (c) ameasure of cardiac ischemia during exercise in said subject, wherein agreater difference between said first and second data sets indicatesgreater cardiac ischemia and lesser cardiac or cardiovascular health insaid subject.
 22. The method according to claim 21, wherein said stageof gradually increasing exercise load and stage of rest are each atleast 3 minutes in duration.
 23. The method according to claim 21,wherein said stage of gradually increasing exercise load and said stageof rest are together carried out for a total time of from 6 minutes to40 minutes.
 24. The method according to claim 21, wherein said stage ofgradually increasing exercise load is carried out at at least threedifferent load levels.
 25. The method according to 21, wherein saidcomparing step is carried out by generating curves from each of saiddata sets.
 26. The method according to 25, wherein said comparing stepis carried out by comparing the shapes of said curves from said datasets.
 27. The method according to claim 25, wherein said comparing stepis carried out by determining a measure of the domain between saidcurves.
 28. The method according to claim 25, wherein said comparingstep is carried out by both comparing the shapes of said curves fromdata sets and determining a measure of the domain between said curves.29. The method according to claim 25, further comprising the step ofdisplaying said curves.
 30. The method according to claim 21, whereinsaid heart rate during said stage of gradually increasing exercise loaddoes not exceed more than 120 beats per minute.
 31. The method accordingto claim 21, wherein said heart rate during said stage of graduallyincreasing heart rate exceeds 120 beats per minute.
 32. The methodaccording to claim 21, further comprising the step of: (e) comparingsaid measure of cardiac ischemia during exercise to at least onereference value; and then (f) generating from said comparison of step(e) a quantitative indicium of cardiac or cardiovascular health for saidsubject.
 33. The method according to claim 32, further comprising thesteps of: (g) treating said subject with a cardiovascular therapy; andthen (h) repeating steps (a) through (f) to assess the efficacy of saidcardiovascular therapy, in which a decrease in the difference betweensaid data sets from before said therapy to after said therapy indicatesan improvement in cardiac or cardiovascular health in said subject fromsaid cardiovascular therapy.
 34. The method according to claim 33,wherein said cardiovascular therapy is selected from the groupconsisting of aerobic exercise, muscle strength building, change indiet, nutritional supplement, weight loss, stress reduction, smokingcessation, pharmaceutical treatment, surgical treatment, andcombinations thereof.
 35. The method according to claim 33, furthercomprising the step of assessing from said quantitative indicium thelikelihood that said subject is at risk to experience a futureischemia-related cardiac incident.
 36. A method of assessing cardiacischemia in a subject to provide a measure of cardiac or cardiovascularhealth in that subject, wherein said subject is afflicted with coronaryartery disease, said method comprising the steps of: (a) collecting afirst RR-interval data set from said subject during a stage of graduallyincreasing exercise load and gradually increasing heart rate at least 5minutes in duration, and at at least three different load levels; andthen, after an abrupt stop in exercise, (b) collecting a secondRR-interval data set from said subject during a stage of rest andgradually decreasing heart rate at least 5 minutes in duration; (c)comparing said first RR-interval data set to said second RR-intervaldata set to determine the difference between said data sets; (d)generating from said comparison of step (c) a measure of cardiacischemia during exercise in said subject, wherein a greater differencebetween said first and second data sets indicates greater cardiacischemia and lesser cardiac or cardiovascular health in said subject;(e) comparing said measure of cardiac ischemia during exercise to atleast one reference value; and then (f) generating from said comparisonof step (e) a quantitative indicium of cardiac or cardiovascular healthfor said subject.
 37. The method according to claim 36, wherein saidstage of gradually increasing exercise load and said stage of rest aretogether carried out for a total time of from 6 minutes to 40 minutes.38. The method according to claim 36, wherein said comparing step iscarried out by generating curves from each of said data sets.
 39. Themethod according to claim 38, wherein said comparing step is carried outby comparing the shapes of said curves from said data sets.
 40. Themethod according to claim 38, wherein said comparing step is carried outby determining a measure of the domain between said curves.
 41. Themethod according to claim 38, wherein said comparing step is carried outby both comparing the shapes of said curves from said data sets anddetermining a measure of the domain between said curves.
 42. The methodaccording to claim 38, further comprising the step of displaying saidcurves.
 43. The method according to claim 36, wherein said heart rateduring said stage of gradually increasing exercise load does not exceedmore than 120 beats per minute.
 44. The method according to claim 36,wherein said heart rate during said stage of gradually increasing heartrate exceeds 120 beats per minute.
 45. The method according to claim 36,further comprising the steps of: (g) treating said subject with acardiovascular therapy; and then (h) repeating steps (a) through (f) toassess the efficacy of said cardiovascular therapy, in which a decreasein the difference between said data sets from before said therapy toafter said therapy indicates an improvement in cardiac or cardiovascularhealth in said subject from said cardiovascular therapy.
 46. The methodaccording to claim 45, wherein said cardiovascular therapy is selectedfrom the group consisting of aerobic exercise, muscle strength building,change in diet, nutritional supplement, weight loss, stress reduction,smoking cessation, pharmaceutical treatment, surgical treatment, andcombinations thereof.
 47. The method according to claim 36, furthercomprising the step of assessing from said quantitative indicium thelikelihood that said subject is at risk to experience a futureischemia-related cardiac incident.